Solve each equation $$ 3 \frac{1}{6}-x=2 \frac{2}{3} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
3 \frac{1}{6} - x = 2 \frac{2}{3}
$$

**Step 1: Convert Mixed Numbers to Improper Fractions**

1. $$ 3 \frac{1}{6} $$:
   $$
   3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6}
   $$

2. $$ 2 \frac{2}{3} $$:
   $$
   2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}
   $$

**Step 2: Rewrite the Equation with Improper Fractions**

$$
\frac{19}{6} - x = \frac{8}{3}
$$

**Step 3: Solve for $$ x $$**

$$
x = \frac{19}{6} - \frac{8}{3}
$$

To subtract the fractions, they need a common denominator. The least common denominator (LCD) of 6 and 3 is 6.

Convert $$ \frac{8}{3} $$ to sixths:

$$
\frac{8}{3} = \frac{16}{6}
$$

Now subtract:

$$
x = \frac{19}{6} - \frac{16}{6} = \frac{3}{6} = \frac{1}{2}
$$

**Final Answer:**

$$
x = \frac{1}{2}
$$
$$ x = \frac{1}{2} $$

Solve each equation \( 3 \frac{1}{6}-x=2 \frac{2}{3} \)