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Math  /  Algebra

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Solve. 10(z−10)=−4010(z-10)=-40
Answer Attempt 1 out of 2 Submit Answer

Studdy Solution

STEP 1

1. The equation 10(z−10)=−40 10(z-10) = -40 is a linear equation in one variable, z z .
2. The goal is to solve for z z .
3. The equation involves basic algebraic operations, including distribution and division.

STEP 2

1. Distribute the constant outside the parentheses.
2. Isolate the variable z z by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the 10 10 across the terms inside the parentheses:
10(z−10)=10z−100 10(z - 10) = 10z - 100
Now the equation is:
10z−100=−40 10z - 100 = -40

STEP 4

To isolate z z , first add 100 100 to both sides of the equation to eliminate the constant term on the left:
10z−100+100=−40+100 10z - 100 + 100 = -40 + 100
This simplifies to:
10z=60 10z = 60

STEP 5

Now, divide both sides by 10 10 to solve for z z :
10z10=6010 \frac{10z}{10} = \frac{60}{10}
This simplifies to:
z=6 z = 6

STEP 6

Check the solution by substituting z=6 z = 6 back into the original equation:
10(6−10)=−40 10(6 - 10) = -40
Simplify inside the parentheses:
10(−4)=−40 10(-4) = -40
Simplify the left-hand side:
−40=−40 -40 = -40
Both sides are equal, confirming that the solution is correct.
The solution is:
6 \boxed{6}

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