Solve the following equation. $$ -\frac{x}{5}-3=1+\frac{x}{5} $$

Question

UpStudy AI · Accepted Answer

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:**
$$
x = -10
$$
$$ x = -10 $$

Solve the following equation.