Question
Solve the following equation. \[ -\frac{x}{5}-3=1+\frac{x}{5} \]
Ask by Clarke Griffin. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -10 \)
Solution
To solve the equation:
\[
-\frac{x}{5} - 3 = 1 + \frac{x}{5}
\]
**Step 1: Eliminate the Fractions**
Multiply every term by 5 to eliminate the denominators:
\[
5 \left( -\frac{x}{5} \right) - 5 \times 3 = 5 \times 1 + 5 \left( \frac{x}{5} \right)
\]
Simplifying each term:
\[
- x - 15 = 5 + x
\]
**Step 2: Get All \( x \)-Terms on One Side**
Add \( x \) to both sides to move all \( x \)-terms to the right:
\[
-15 = 5 + x + x
\]
\[
-15 = 5 + 2x
\]
**Step 3: Isolate \( x \)**
Subtract 5 from both sides:
\[
-15 - 5 = 2x
\]
\[
-20 = 2x
\]
Divide both sides by 2:
\[
x = \frac{-20}{2}
\]
\[
x = -10
\]
**Solution:**
\[
x = -10
\]
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Simplify this solution Mind Expander
To solve the equation \(-\frac{x}{5} - 3 = 1 + \frac{x}{5}\), we first eliminate the fractions by multiplying the entire equation by 5. This gives us: \[ -5 \cdot \frac{x}{5} - 5 \cdot 3 = 5 \cdot 1 + 5 \cdot \frac{x}{5} \] Which simplifies to: \[ -x - 15 = 5 + x \] Next, we can rearrange the equation by adding \(x\) to both sides and adding 15 to both sides: \[ -x + x - 15 + 15 = 5 + x + 15 \] This results in: \[ 0 = x + 20 \] Now we can isolate \(x\) by subtracting 20 from both sides: \[ x = -20 \] Thus, the solution to the equation is: \[ \boxed{-20} \]
