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Math  /  Algebra

Question−8=x+11−2-8=\frac{x+11}{-2}

Studdy Solution

STEP 1

1. The equation −8=x+11−2 -8 = \frac{x+11}{-2} involves a linear equation with one variable.
2. The goal is to solve for x x .
3. The equation involves basic algebraic operations, specifically multiplication and addition/subtraction.

STEP 2

1. Eliminate the fraction by performing multiplication.
2. Isolate the variable x x by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

To eliminate the fraction, multiply both sides of the equation by −2-2 to clear the denominator:
−8×(−2)=x+11−2×(−2) -8 \times (-2) = \frac{x+11}{-2} \times (-2)

STEP 4

Simplify both sides:
16=x+11 16 = x + 11

STEP 5

Now, isolate x x by subtracting 11 from both sides of the equation:
16−11=x+11−11 16 - 11 = x + 11 - 11

STEP 6

Simplify both sides:
5=x 5 = x

STEP 7

Check the solution by substituting x=5 x = 5 back into the original equation:
−8=5+11−2 -8 = \frac{5 + 11}{-2}

STEP 8

Simplify the right-hand side:
−8=16−2 -8 = \frac{16}{-2}
−8=−8 -8 = -8
Both sides are equal, confirming that the solution is correct.
The solution is:
5 \boxed{5}

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