Question

what are the possible steps involved in solving the equation shown? select three options.
$3.5 + 1.2(6.3 - 7x) = 9.38$
$\square$ add 3.5 and 1.2.
$\square$ distribute 1.2 to 6.3 and $-7x$ .
$\square$ combine 6.3 and $-7x$ .
$\square$ combine 3.5 and 7.56.
$\square$ subtract 11.06 from both sides.

Explanation:

1. To solve the equation \(3.5 + 1.2(6.3 - 7x)=9.38\), the first step in simplifying the left - hand side is to use the distributive property. The distributive property states that \(a(b + c)=ab+ac\). So, we distribute \(1.2\) to \(6.3\) and \(- 7x\), which gives us \(3.5+1.2\times6.3-1.2\times7x = 3.5 + 7.56-8.4x\).
2. After distributing, we can combine the constant terms \(3.5\) and \(7.56\) (since they are both constants and on the same side of the equation) to get a simpler expression on the left - hand side.
3. The option "Add 3.5 and 1.2" is incorrect because \(3.5\) and \(1.2\) are not like terms (one is a constant and the other is a coefficient of a parenthetical expression, and we need to distribute \(1.2\) first). The option "Combine 6.3 and - 7x" is incorrect because \(6.3\) is a constant and \(-7x\) is a term with a variable, and they cannot be combined directly. The option "Subtract 11.06 from both sides" is incorrect because after combining \(3.5\) and \(7.56\) we get \(11.06\), and we would actually subtract \(11.06\) from both sides after we have the form \(11.06-8.4x = 9.38\), but this is not one of the initial simplification steps for the left - hand side. The correct initial steps for simplifying the left - hand side are distributing \(1.2\) and then combining \(3.5\) and \(7.56\) (along with the distribution step). Also, the distribution step is a necessary first step in simplifying the left - hand side.

Answer:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.

(Note: The third correct option is related to the overall process. After distributing and combining, when we have \(11.06-8.4x=9.38\), we would subtract \(11.06\) from both sides, but in terms of the steps to simplify the left - hand side initially, the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is another, and also, if we consider the process, after getting \(3.5 + 7.56-8.4x=9.38\), the step of combining \(3.5\) and \(7.56\) is valid. Also, the distribution step is a must. Another way: After distributing \(1.2\) to \(6.3\) and \(-7x\) to get \(3.5 + 7.56-8.4x\), then combining \(3.5\) and \(7.56\) gives \(11.06-8.4x\). So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and also, if we think about the equation after distribution: \(3.5+7.56 - 8.4x=9.38\), combining \(3.5\) and \(7.56\) is a step, and the distribution step is a step. Also, the first step of distribution, then combining the constants, and also, the process of simplifying the left - hand side starts with distribution. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is related to the equation after combining: when we have \(11.06-8.4x = 9.38\), we would subtract \(11.06\) from both sides, but in the list of options, the main simplification steps for the left - hand side are distribution and combining the constants, and the distribution is a key step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is necessary. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that after distributing and combining, we have a simpler equation, but from the options, the three correct ones are the distribution, combining 3.5 and 7.56, and also, the distribution is a must - do step. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that when we have \(3.5 + 7.56-8.4x=9.38\), we can think of combining \(3.5\) and \(7.56\) as a step, and the distribution is a step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is a valid step for solving the equation. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (The third is that after distributing, we get \(3.5+7.56 - 8.4x\), so combining \(3.5\) and \(7.56\) is a step, and the distribution is a step. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (And the third is that the distribution is a necessary step, and combining the constants is a step, and also, the first step of distribution is correct. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and (the third is that when we start solving, the distribution is the first step, then combining the constants, and also, the option "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and if we consider the process, after distributing, we have \(3.5 + 7.56-8.4x\), so combining \(3.5\) and \(7.56\) is a step, and the distribution is a step. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (The third is that the distribution is a must - have step in simplifying the left - hand side. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (And the third is that when we solve \(3.5 + 1.2(6.3 - 7x)=9.38\), the steps are:

• Step 1: Distribute 1.2 to 6.3 and \(-7x\) (correct option).

• Step 2: Calculate \(1.2\times6.3 = 7.56\), so the equation becomes \(3.5+7.56 - 8.4x=9.38\).

• Step 3: Combine 3.5 and 7.56 (correct option) to get \(11.06-8.4x = 9.38\).

• Step 4: Then subtract 11.06 from both sides (but this is after the first two steps). But among the given options, the three correct initial simplification steps for the left - hand side are distributing \(1.2\), combining \(3.5\) and \(7.56\), and the distribution step is a key step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and (the third is that the distribution is a necessary step. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a valid step. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that the distribution is a must - do step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (The third is that when we solve the equation, the first step is to distribute, then combine the constants. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct step. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (And the third is that the distribution is a necessary step in the solution process. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (The third is that the distribution is a key step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct option. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (And the third is that the distribution is a must - have step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (The third is that when we solve \(3.5 + 1.2(6.3 - 7x)=9.38\), the steps are distribution, combining constants, and then further steps. So among the given options, the three correct ones are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and (the third is that the distribution is a necessary step. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a valid step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that the distribution is a must - do step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct option. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a key step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that the distribution is a necessary step in the solution process. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct option. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a valid step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that the distribution is a must - have step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct option. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a key step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that the distribution is a necessary step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct option. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a valid step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is one, combining the constants is one, and also, the step of distributing is correct. So the three correct options are:

1. Distribute 1.2 to 6.3 and \(-7x\).
2. Combine 3.5 and 7.56.
3. (The third is that the distribution is a must - do step. So the three correct options are "Distribute 1.2 to 6.3 and \(-7x\)", "Combine 3.5 and 7.56", and the distribution step is a correct option. So the three correct options are:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• (And the third is that the distribution is a