Math  /  Algebra

QuestionWhich value of nn makes the equation true? 12n=8-\frac{1}{2} n=-8 A. -16 B. -4 C. 4 D. 16

Studdy Solution

STEP 1

1. The equation 12n=8 -\frac{1}{2} n = -8 is asking us to solve for n n .
2. This is a one-step equation with one solution.
3. The equation involves basic algebraic operations, specifically multiplication and division.

STEP 2

1. Understand the equation and what it represents.
2. Isolate the variable n n by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.
4. Compare the solution with the given options.

STEP 3

The equation 12n=8 -\frac{1}{2} n = -8 tells us that n n is multiplied by 12 -\frac{1}{2} to give 8 -8 .

STEP 4

To isolate n n , we need to perform the opposite operation of multiplying by 12 -\frac{1}{2} , which is dividing by 12 -\frac{1}{2} or multiplying by the reciprocal, 2-2:
n=8×(2) n = -8 \times (-2)

STEP 5

Simplify the right-hand side:
n=16 n = 16

STEP 6

Check the solution by substituting n=16 n = 16 back into the original equation:
12×16=8 -\frac{1}{2} \times 16 = -8

STEP 7

Simplify the left-hand side:
8=8 -8 = -8
The equation holds true, confirming our solution.

STEP 8

Compare the solution n=16 n = 16 with the given options:
A. -16 B. -4 C. 4 D. 16
The correct option is D. 16.

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