Question
What is the solution to the equation shown below? \[ 2.5(x+5)=7.5 x-0.5 \] \( x=2.6 \) \( x=1.1 \) \( x=-2.6 \) \( x=-1.1 \)
Ask by Barker Mathis. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 2.6 \)
Solution
To solve the equation:
\[
2.5(x + 5) = 7.5x - 0.5
\]
**Step 1: Distribute the 2.5 on the left side.**
\[
2.5x + 12.5 = 7.5x - 0.5
\]
**Step 2: Move all terms involving \( x \) to one side and constant terms to the other.**
Subtract \( 2.5x \) from both sides:
\[
12.5 = 5x - 0.5
\]
Add \( 0.5 \) to both sides:
\[
13 = 5x
\]
**Step 3: Solve for \( x \).**
Divide both sides by 5:
\[
x = \frac{13}{5} = 2.6
\]
**Answer:**
\( x = 2.6 \)
**Correct Option:**
\( x=2.6 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the equation \( 2.5(x+5)=7.5 x-0.5 \), you’ll want to first distribute the \( 2.5 \) on the left-hand side, giving you \( 2.5x + 12.5 = 7.5x - 0.5 \). Next, you can move all the \( x \) terms to one side by subtracting \( 2.5x \) from both sides, resulting in \( 12.5 = 5x - 0.5 \). Adding \( 0.5 \) to both sides leads to \( 13 = 5x \), and dividing by \( 5 \) gives \( x = 2.6 \). Now, to avoid common mistakes in future calculations, double-check your distributions and combine like terms carefully! It’s also a good practice to verify your solution by substituting it back into the original equation—just plug in \( x=2.6 \) and see if both sides balance. Happy solving!
