Question
Write the other side of this equation so that it is true for all values of \( x \). \( \frac{1}{2}(6 x-10)-x= \)
Ask by Guerrero Turnbull. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The other side of the equation is \( 2x - 5 \).
Solution
To make the equation true for all values of \( x \), let's simplify the left side and express it in an equivalent form.
Given:
\[
\frac{1}{2}(6x - 10) - x
\]
**Step 1: Distribute the \(\frac{1}{2}\)**
\[
\frac{1}{2} \times 6x - \frac{1}{2} \times 10 - x = 3x - 5 - x
\]
**Step 2: Combine like terms**
\[
3x - x - 5 = 2x - 5
\]
**Final Equation:**
\[
\frac{1}{2}(6x - 10) - x = 2x - 5
\]
So, the other side of the equation that makes it true for all \( x \) is:
\[
2x - 5
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the other side of the equation that makes it true for all values of \( x \), we start by simplifying the left side. First, distribute \( \frac{1}{2} \): \[ \frac{1}{2}(6x - 10) = 3x - 5 \] Now, substitute this back into the equation: \[ 3x - 5 - x = 3x - x - 5 = 2x - 5 \] Therefore, the complete equation is: \[ \frac{1}{2}(6x - 10) - x = 2x - 5 \] So, the other side of the equation is \( 2x - 5 \).
