Math  /  Algebra

Question15) 6=8+p4-6=-8+\frac{p}{4}

Studdy Solution

STEP 1

1. The equation 6=8+p4 -6 = -8 + \frac{p}{4} is asking us to solve for p p .
2. This is a linear equation involving a fraction.
3. The goal is to isolate the variable p p .

STEP 2

1. Isolate the fractional term.
2. Eliminate the fraction by multiplying.
3. Solve for p p .

STEP 3

To isolate the fractional term, we need to get rid of the 8-8 on the right side of the equation. We can do this by adding 88 to both sides:
6+8=8+p4+8 -6 + 8 = -8 + \frac{p}{4} + 8

STEP 4

Simplify both sides:
2=p4 2 = \frac{p}{4}

STEP 5

To eliminate the fraction, multiply both sides of the equation by 44:
4×2=4×p4 4 \times 2 = 4 \times \frac{p}{4}

STEP 6

Simplify both sides:
8=p 8 = p

STEP 7

Check the solution by substituting p=8 p = 8 back into the original equation:
6=8+84 -6 = -8 + \frac{8}{4}

STEP 8

Simplify the right side:
6=8+2 -6 = -8 + 2
6=6 -6 = -6
Both sides are equal, confirming that the solution is correct.
The solution is:
8 \boxed{8}

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