Question

1
select the correct answer from each drop-down menu.
consider the equation below.
-2(5x + 8) = 14 + 6x
the equation was solved using the following steps.
step 1: -10x - 16 = 14 + 6x
step 2: -16x - 16 = 14
step 3: -16x = 30
step 4: x = 30/-16
step 5: x = -15/8
complete the statements below with the process used to achieve steps 1-4.
step 1: drop-down -2 to 5x and 8.
step 2: drop-down 6x.
step 3: drop-down 16.
step 4: drop-down -16.
drop-down options: divide by, subtract, multiply by, add
reset next

Explanation:

Step 1 Analysis:

To get from \(-2(5x + 8)\) to \(-10x - 16\), we use the Distributive Property (which is a form of multiplication). We multiply \(-2\) by \(5x\) and \(-2\) by \(8\). So the operation here is "Multiply by" (since we're distributing the \(-2\) through the parentheses, which is multiplication).

Step 2 Analysis:

To get from \(-10x - 16 = 14 + 6x\) to \(-16x - 16 = 14\), we need to eliminate \(6x\) from the right - hand side. We do this by subtracting \(6x\) from both sides of the equation. So the operation here is "Subtract" (we subtract \(6x\) from both sides).

Step 3 Analysis:

To get from \(-16x - 16 = 14\) to \(-16x = 30\), we need to eliminate \(-16\) from the left - hand side. We do this by adding \(16\) to both sides of the equation (because \(-16+16 = 0\)). So the operation here is "Add" (we add \(16\) to both sides).

Step 4 Analysis:

To get from \(-16x=30\) to \(x = \frac{30}{-16}\), we need to isolate \(x\). We do this by dividing both sides of the equation by \(-16\) (since \(\frac{-16x}{-16}=x\)). So the operation here is "Divide by".

Final Answers for Each Step:

• Step 1: Multiply by
• Step 2: Subtract
• Step 3: Add
• Step 4: Divide by

Answer:

Step 1 Analysis:

To get from \(-2(5x + 8)\) to \(-10x - 16\), we use the Distributive Property (which is a form of multiplication). We multiply \(-2\) by \(5x\) and \(-2\) by \(8\). So the operation here is "Multiply by" (since we're distributing the \(-2\) through the parentheses, which is multiplication).

Step 2 Analysis:

To get from \(-10x - 16 = 14 + 6x\) to \(-16x - 16 = 14\), we need to eliminate \(6x\) from the right - hand side. We do this by subtracting \(6x\) from both sides of the equation. So the operation here is "Subtract" (we subtract \(6x\) from both sides).

Step 3 Analysis:

To get from \(-16x - 16 = 14\) to \(-16x = 30\), we need to eliminate \(-16\) from the left - hand side. We do this by adding \(16\) to both sides of the equation (because \(-16+16 = 0\)). So the operation here is "Add" (we add \(16\) to both sides).

Step 4 Analysis:

To get from \(-16x=30\) to \(x = \frac{30}{-16}\), we need to isolate \(x\). We do this by dividing both sides of the equation by \(-16\) (since \(\frac{-16x}{-16}=x\)). So the operation here is "Divide by".

Final Answers for Each Step:

• Step 1: Multiply by
• Step 2: Subtract
• Step 3: Add
• Step 4: Divide by