Question

Solve the following equation for A: 2A/3 = 8 + 4A

• A. -2.4
• B. 2.4
• C. 1.3
• D. -1.3
• E. 0

Hint:

When solving equations with fractions, multiplying the entire equation by the least common denominator of all fractions is an effective first step to simplify the problem.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The goal is to solve a linear equation for the variable A. This involves isolating A on one side of the equation.
Step 2: Key Formula or Approach:
We will use algebraic manipulation to solve for A. The steps are: 1. Eliminate any fractions.
2. Gather all terms with A on one side of the equation.
3. Gather all constant terms on the other side.
4. Solve for A.
Step 3: Detailed Explanation:
The given equation is: \[ \frac{2A}{3} = 8 + 4A \] First, to eliminate the fraction, multiply both sides of the equation by 3: \[ 3 \times \left(\frac{2A}{3}\right) = 3 \times (8 + 4A) \] \[ 2A = 24 + 12A \] Next, gather all terms with A on one side. Subtract 12A from both sides: \[ 2A - 12A = 24 \] \[ -10A = 24 \] Finally, solve for A by dividing both sides by -10: \[ A = \frac{24}{-10} \] \[ A = -2.4 \] Step 4: Final Answer:
The value of A is -2.4. The correct option is (A).