Question

If 5x + 32 = 4 - 2x, what is the value of x?

• A. -4
• B. -3
• C. 4
• D. 7
• E. 12

Hint:

When solving linear equations, perform inverse operations to isolate the variable. For example, to undo addition, you subtract; to undo multiplication, you divide. Aim to perform these steps systematically to avoid calculation errors.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question asks to solve a linear equation for the variable x. A linear equation is an equation in which the highest power of the variable is one. The goal is to isolate x on one side of the equation.
Step 2: Key Approach:
We will use algebraic manipulation to solve for x. The standard approach is to gather all terms involving x on one side of the equation and all constant terms on the other side.
Step 3: Detailed Explanation:
We are given the equation:
\[ 5x + 32 = 4 - 2x \] First, add 2x to both sides of the equation to move all x terms to the left side.
\[ (5x + 2x) + 32 = 4 - 2x + 2x \] \[ 7x + 32 = 4 \] Next, subtract 32 from both sides of the equation to move all constant terms to the right side.
\[ 7x + 32 - 32 = 4 - 32 \] \[ 7x = -28 \] Finally, divide both sides by 7 to solve for x.
\[ \frac{7x}{7} = \frac{-28}{7} \] \[ x = -4 \] Step 4: Final Answer:
The value of x that satisfies the equation is -4. Therefore, the correct answer is (A).