Solve for all values of $$ x $$ in simplest form. $$ 4|10-3 x|+3=51 $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
4|10 - 3x| + 3 = 51
$$

Follow these steps:

1. **Isolate the absolute value term:**
   $$
   4|10 - 3x| = 51 - 3
   $$
   $$
   4|10 - 3x| = 48
   $$

2. **Divide both sides by 4:**
   $$
   |10 - 3x| = 12
   $$

3. **Set up two separate equations based on the absolute value:**
   $$
   10 - 3x = 12 \quad \text{or} \quad 10 - 3x = -12
   $$

4. **Solve each equation separately:**

- **First equation:**
     $$
     10 - 3x = 12
     $$
     $$
     -3x = 2
     $$
     $$
     x = -\frac{2}{3}
     $$

- **Second equation:**
     $$
     10 - 3x = -12
     $$
     $$
     -3x = -22
     $$
     $$
     x = \frac{22}{3}
     $$

**Solution:**
$$
x = -\frac{2}{3} \quad \text{or} \quad x = \frac{22}{3}
$$
The solutions are $$ x = -\frac{2}{3} $$ and $$ x = \frac{22}{3} $$.

Solve for all values of \( x \) in simplest form. \[ 4|10-3 x|+3=51 \]