Ortiz Montgomery
07/10/2023 · Middle School
Check to see whether the given value is a solution to the equation. \( \frac{1-3 z}{8}=\frac{10-2 z}{10} ; z=-5 \) It is a solution. It is not a solution.
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To check whether \( z = -5 \) is a solution to the equation
\[
\frac{1-3z}{8} = \frac{10-2z}{10},
\]
we will substitute \( z = -5 \) into the equation and see if both sides are equal.
First, substitute \( z = -5 \) into the left side of the equation:
\[
\frac{1 - 3(-5)}{8} = \frac{1 + 15}{8} = \frac{16}{8} = 2.
\]
Now, substitute \( z = -5 \) into the right side of the equation:
\[
\frac{10 - 2(-5)}{10} = \frac{10 + 10}{10} = \frac{20}{10} = 2.
\]
Now we compare both sides:
Left side: \( 2 \)
Right side: \( 2 \)
Since both sides are equal, we conclude that
\[
\frac{1-3(-5)}{8} = \frac{10-2(-5)}{10}.
\]
Thus, \( z = -5 \) is indeed a solution to the equation.
The answer is: **It is a solution.**
Quick Answer
z=-5 is a solution to the equation.
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