Solve the equation. Check the solution. 1/2 = -1/8d. d = (simplify your answer.)

Understand the Problem

The question is asking to solve the equation 1/2 = -1/8d for the variable d and to simplify the answer.

Answer

$d = -4$

Steps to Solve

Multiply both sides by -8 To isolate $d$ in the equation $ \frac{1}{2} = -\frac{1}{8}d $, multiply both sides by $-8$ to eliminate the fraction on the right side.

$$ -8 \cdot \frac{1}{2} = d $$

Simplify the left side Now simplify the left side:

$$ -8 \cdot \frac{1}{2} = -4 $$

Thus, we have:

$$ d = -4 $$

Check the solution Substitute $d = -4$ back into the original equation to verify:

$$ \frac{1}{2} = -\frac{1}{8}(-4) $$

Calculate the right side:

$$ -\frac{1}{8} \cdot -4 = \frac{4}{8} = \frac{1}{2} $$

Since both sides are equal, our solution is confirmed.

The simplified answer is $d = -4$.

More Information

In this problem, we solved for the variable by isolating it through multiplication and verification. The solution indicates that for the initial condition, the variable takes on a negative value.

Tips

Not multiplying by the negative correctly, which can lead to sign errors.
Forgetting to check the solution may cause mistrust in the result.

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