Question

svlc algebra 1a - standard (15260)
solving linear equations: variable on one side
what are the possible steps involved in solving the equation shown? choose three correct answers.
$3.5 + 1.2(6.3 - 7x) = 9.38$

• add 3.5 and 1.2.
• distribute 1.2 to 6.3 and $-7x$.
• combine 6.3 and $-7x$.
• combine 3.5 and 7.56.
• subtract 11.06 from both sides.

Explanation:

To solve the linear equation \( 3.5 + 1.2(6.3 - 7x) = 9.38 \), we analyze each option:

Step 1: Analyze "Distribute 1.2 to 6.3 and \(-7x\)"

Using the distributive property \( a(b + c) = ab + ac \), distributing \( 1.2 \) to \( 6.3 \) and \( -7x \) gives:
\( 1.2 \times 6.3 = 7.56 \) and \( 1.2 \times (-7x) = -8.4x \).
This is a valid first step to eliminate the parentheses.

Step 2: Analyze "Combine 3.5 and 7.56"

After distributing \( 1.2 \), the equation becomes \( 3.5 + 7.56 - 8.4x = 9.38 \).
Combining the constant terms \( 3.5 + 7.56 = 11.06 \) simplifies the equation to \( 11.06 - 8.4x = 9.38 \).
This is a valid step to combine like terms.

Step 3: Analyze "Subtract 11.06 from both sides"

From \( 11.06 - 8.4x = 9.38 \), subtracting \( 11.06 \) from both sides isolates the term with \( x \):
\( 11.06 - 8.4x - 11.06 = 9.38 - 11.06 \), which simplifies to \( -8.4x = -1.68 \).
This is a valid step to solve for \( x \).

Eliminate Incorrect Options:

• "Add 3.5 and 1.2": \( 3.5 \) and \( 1.2 \) are not like terms (one is a constant, the other is a coefficient), so this is invalid.
• "Combine 6.3 and \(-7x\)": \( 6.3 \) (a constant) and \( -7x \) (a term with \( x \)) cannot be combined, so this is invalid.

• "Distribute 1.2 to 6.3 and \(-7x\)" is valid (applies the distributive property).
• "Combine 3.5 and 7.56" is valid (combines constant terms after distribution).
• "Subtract 11.06 from both sides" is valid (isolates the variable term).

Answer:

• Distribute 1.2 to 6.3 and \(-7x\).
• Combine 3.5 and 7.56.
• Subtract 11.06 from both sides.