Solve the following equation. $$ -4-\frac{1}{4} x=1+\frac{1}{3} x $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
-4 - \frac{1}{4}x = 1 + \frac{1}{3}x
$$

**Step 1: Move all terms containing $$ x $$ to one side and constants to the other side.**

$$
-4 - 1 = \frac{1}{3}x + \frac{1}{4}x
$$

Simplify the constants:

$$
-5 = \frac{1}{3}x + \frac{1}{4}x
$$

**Step 2: Combine like terms on the right side.**

To add the fractions $$\frac{1}{3}x$$ and $$\frac{1}{4}x$$, find a common denominator, which is 12.

$$
\frac{1}{3}x = \frac{4}{12}x \
\frac{1}{4}x = \frac{3}{12}x
$$

Now, add them together:

$$
\frac{4}{12}x + \frac{3}{12}x = \frac{7}{12}x
$$

So the equation becomes:

$$
-5 = \frac{7}{12}x
$$

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

Multiply both sides by $$ \frac{12}{7} $$ to isolate $$ x $$:

$$
x = -5 \times \frac{12}{7}
$$

$$
x = -\frac{60}{7}
$$

**Step 4: Simplify the solution (if desired).**

$$
x = -\frac{60}{7} \approx -8.57
$$

**Final Answer:**

$$
x = -\frac{60}{7} \quad \text{or approximately} \quad -8.57
$$
$$ x = -\frac{60}{7} $$

Solve the following equation. \[ -4-\frac{1}{4} x=1+\frac{1}{3} x \]