Question

Solve for z: \(3(z + 4) - 7 = 17\)

• A. 4
• B. 8
• C. 2
• D. -8
• E. -2

Hint:

When a term in parentheses is multiplied by a constant, you have two options: distribute the constant, or divide the other side of the equation by the constant. Look ahead to see which path is easier. If the number on the other side is a multiple of the constant, dividing first can save you a step.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a basic algebra problem that requires solving a linear equation for an unknown variable, z.
Step 2: Key Formula or Approach:
We will use the order of operations in reverse to isolate z. The steps are: 1. Add or subtract constants to isolate the term with the variable. 2. Distribute multiplication over parentheses. 3. Combine like terms. 4. Divide to solve for the variable.
Step 3: Detailed Explanation:
The given equation is: \[ 3(z + 4) - 7 = 17 \] First, add 7 to both sides of the equation to isolate the term with the parenthesis: \[ 3(z + 4) = 17 + 7 \] \[ 3(z + 4) = 24 \] Next, we can either distribute the 3 or divide both sides by 3. Dividing is simpler here. \[ z + 4 = \frac{24}{3} \] \[ z + 4 = 8 \] Finally, subtract 4 from both sides to solve for z: \[ z = 8 - 4 \] \[ z = 4 \] Step 4: Final Answer:
The value of z is 4.