Question

Find \(x\): \(4(x - 2) = 3(x + 5)\).

• A. \(23\)
• B. \(17\)
• C. \(13\)
• D. \(7\)

Hint:

First expand both brackets using the distributive property, then bring all x-terms to one side and the constants to the other side before dividing to isolate x. Keep track of your signs carefully when moving terms across the equals sign.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The task is to find the value of the unknown variable \(x\) that satisfies the given linear equation.
Step 2: Key Formula or Approach:
Apply the distributive property \(a(b + c) = ab + ac\) to remove parentheses, and then isolate the variable.
Step 3: Detailed Explanation:
Expand both sides of the equation:
\[ 4x - 8 = 3x + 15 \]
Group the \(x\) terms on the left side and the constant terms on the right side:
\[ 4x - 3x = 15 + 8 \]
Simplify both sides:
\[ x = 23 \]
Step 4: Final Answer:
The value of \(x\) is \(23\).