Question

question 3
for the following solution of a linear equation, determine what was done at each step:
$11x - 3 = 52$ initial problem
$11x = 55$ step 1
$x = 5$ step 2
\\(box\\) step 2: divide by 11
\\(box\\) step 1: add 3 to both sides
\\(box\\) step 1: add 3
\\(box\\) step 1: subtract 3 from both sides
\\(box\\) step 2: multiply both sides by 11
\\(box\\) step 2: divide both sides by 11

Explanation:

• For Step 1: The initial equation is \(11x - 3 = 52\). To get to \(11x = 55\), we add 3 to both sides (since \(-3 + 3 = 0\) on the left, and \(52+3 = 55\) on the right), so "Step 1: Add 3 to both sides" is correct.
• For Step 2: The equation is \(11x = 55\). To solve for \(x\), we divide both sides by 11 (since \(\frac{11x}{11}=x\) and \(\frac{55}{11} = 5\)), so "Step 2: Divide both sides by 11" is correct. Also, "Step 2: Divide by 11" is a simpler way to express the same operation (implied on both sides), so it is also correct.

Answer:

Step 1: Add 3 to both sides
Step 2: Divide by 11 (or Step 2: Divide both sides by 11)