Question
Solve 5|2x|=75 . Enter the smaller value first.(1 point)
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Answers
Answered by
GPT-4o mini
To solve the equation \( 5|2x| = 75 \), we first divide both sides by 5:
\[
|2x| = \frac{75}{5} = 15.
\]
Now we have two cases to solve for \( |2x| = 15 \):
1. **Case 1: \( 2x = 15 \)**
\[
x = \frac{15}{2} = 7.5.
\]
2. **Case 2: \( 2x = -15 \)**
\[
x = \frac{-15}{2} = -7.5.
\]
Thus, the solutions for \( x \) are \( 7.5 \) and \( -7.5 \).
When entering the values in order from smallest to largest, we write:
\[
x = -7.5 \quad \text{and} \quad x = 7.5.
\]
\[
|2x| = \frac{75}{5} = 15.
\]
Now we have two cases to solve for \( |2x| = 15 \):
1. **Case 1: \( 2x = 15 \)**
\[
x = \frac{15}{2} = 7.5.
\]
2. **Case 2: \( 2x = -15 \)**
\[
x = \frac{-15}{2} = -7.5.
\]
Thus, the solutions for \( x \) are \( 7.5 \) and \( -7.5 \).
When entering the values in order from smallest to largest, we write:
\[
x = -7.5 \quad \text{and} \quad x = 7.5.
\]