Examkin

Question

Difficulty: MediumSolving One-Variable Linear Equations
If 3(p+4)2−7=2p−4 \frac{3(p + 4)}{2} - 7 = 2p - 4 what is the value of pp?
  1. A
    13
  2. B
    18
  3. C
    -2
  4. 6Answer

Answer

6
The correct answer is found by first isolating the fractional term by adding 7 to both sides, then multiplying the entire equation by 2 to eliminate the denominator, distributing properly, and finally moving variables to one side and constants to the other to solve for p.

Step-by-Step Solution

1
Add 7 to both sides of the equation.
3(p+4)2=2p+3 \frac{3(p + 4)}{2} = 2p + 3
This isolates the fractional term on the left side of the equation.
2
Multiply both sides by 2.
3(p+4)=4p+6 3(p + 4) = 4p + 6
This clears the denominator from the fraction.
3
Distribute the 3 on the left side.
3p+12=4p+6 3p + 12 = 4p + 6
This expands the parentheses so like terms can be combined.
4
Subtract 3p from both sides.
12=p+6 12 = p + 6
This groups all variable terms on the right side of the equation.
5
Subtract 6 from both sides.
p=6 p = 6
This isolates the variable p to find its final value.

Key Concept

Solving Linear Equations with Fractions
Rate this question

Topics

Solving One-Variable Linear Equations

More questions from this topic