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Math  /  Algebra

QuestionSolve for zz. 9=−21−1011z9=-21-\frac{10}{11} z
Answer Attempt 1 out of 2 z=z= □\square Submit Answer

Studdy Solution

STEP 1

1. The equation 9=−21−1011z 9 = -21 - \frac{10}{11} z is asking us to solve for z z .
2. This is a linear equation with one variable.
3. The equation involves basic algebraic operations, specifically addition and multiplication.

STEP 2

1. Isolate the term involving z z .
2. Solve for z z by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.

STEP 3

To isolate the term involving z z , we need to eliminate the constant term on the right side of the equation. Add 21 to both sides:
9+21=−21+21−1011z 9 + 21 = -21 + 21 - \frac{10}{11} z

STEP 4

Simplify the left side:
30=−1011z 30 = -\frac{10}{11} z

STEP 5

To solve for z z , we need to eliminate the coefficient of z z , which is −1011-\frac{10}{11}. Multiply both sides by the reciprocal of −1011-\frac{10}{11}, which is −1110-\frac{11}{10}:
30×(−1110)=z 30 \times \left(-\frac{11}{10}\right) = z

STEP 6

Simplify the left side:
z=−33010 z = -\frac{330}{10}
z=−33 z = -33

STEP 7

Verify the solution by substituting z=−33 z = -33 back into the original equation:
9=−21−1011(−33) 9 = -21 - \frac{10}{11}(-33)

STEP 8

Calculate the right side:
9=−21+30 9 = -21 + 30
9=9 9 = 9
Both sides are equal, confirming the solution is correct.
The solution is:
−33 \boxed{-33}

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