Math 7B. Pattering and Algebraic Reasoning. Spring25 Sample work

Question

Question 4
An inequality is shown.
2x - 2 < 4
Correctly order the steps used to solve the inequality.
Step 1
Step 2
Graph the solution

Answer 1

To solve the inequality \(2x - 2 < 4\), we can break it down into clear steps. Here’s how to correctly order the steps:

Step 1

Add 2 to both sides of the inequality: \[ 2x - 2 + 2 < 4 + 2 \] This simplifies to: \[ 2x < 6 \]

Step 2

Divide both sides by 2: \[ \frac{2x}{2} < \frac{6}{2} \] This simplifies to: \[ x < 3 \]

Step 3

Graph the solution: On the number line, you would make an open circle at 3 (to indicate that 3 is not included in the solution) and draw a line to the left to show all numbers less than 3.

Summary of Steps:

1. Add 2 to both sides: \(2x - 2 + 2 < 4 + 2\) → \(2x < 6\)
2. Divide both sides by 2: \( \frac{2x}{2} < \frac{6}{2}\) → \(x < 3\)
3. Graph the solution \(x < 3\) on a number line.

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