Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -\frac{36}{5} \) or \( x = -7.2 \)
Solution
To solve the equation for \( x \):
\[
\frac{5}{6}x + 3 = -3
\]
**Step 1: Subtract 3 from both sides**
\[
\frac{5}{6}x + 3 - 3 = -3 - 3
\]
\[
\frac{5}{6}x = -6
\]
**Step 2: Multiply both sides by the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\)**
\[
\left(\frac{5}{6}x\right) \times \frac{6}{5} = -6 \times \frac{6}{5}
\]
\[
x = -\frac{36}{5}
\]
**Step 3 (Optional): Simplify the fraction**
\[
x = -7 \frac{1}{5} \quad \text{or} \quad x = -7.2
\]
**Solution:**
\[
x = -\frac{36}{5} \quad \text{or} \quad x = -7.2
\]
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Simplify this solution Beyond the Answer
To solve for \( x \), start by isolating the term with \( x \) on one side. First, subtract 3 from both sides of the equation: \[ \frac{5}{6} x + 3 - 3 = -3 - 3 \] This simplifies to: \[ \frac{5}{6} x = -6 \] Next, to eliminate the fraction, multiply both sides by the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\): \[ x = -6 \times \frac{6}{5} \] Calculating this gives: \[ x = -\frac{36}{5} \] So, the solution is: \[ x = -7.2 \]
