Question

2.7 module 2 post-test

put the following steps in order to solve for x:

(3x + 7 = 2x + 12)

• subtract 2x from both sides
• (x = 5)
• subtract 7 from both sides
• divide both sides by 3

Explanation:

Analyze the given equation

We are given the linear equation:

$$3x + 7 = 2x + 12$$

Our goal is to isolate the variable \(x\) using the concepts of Solving Multi-Step Equations.

Subtract 2x from both sides

Using the Solving Multi-Step Equations knowledge point, we first group the variable terms on one side. Subtracting \(2x\) from both sides simplifies the equation:

$$(3x - 2x) + 7 = (2x - 2x) + 12$$

$$x + 7 = 12$$

Subtract 7 from both sides

Next, we isolate the variable \(x\) by moving the constant terms to the other side. Subtracting \(7\) from both sides gives:

$$x + 7 - 7 = 12 - 7$$

$$x = 5$$

Identify the correct sequence

Reviewing the steps provided in the problem:

1. "Subtract 2x from both sides" leads to \(x + 7 = 12\).
2. "Subtract 7 from both sides" leads to \(x = 5\).
3. "x = 5" is the final solution.

The step "Divide both sides by 3" is not needed to solve this equation.

Answer:

The correct order of the steps to solve for \(x\) is:

1. Subtract 2x from both sides
2. Subtract 7 from both sides
3. \(x = 5\)

(Note: "Divide both sides by 3" is an extra step and is not used in this solution.)