Question 2 Solve the absolute val $$ |3 x-5|=11 $$ $$ \square $$ and $$ \square $$ Submit Question

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UpStudy AI · Accepted Answer

To solve the equation $$ |3x - 5| = 11 $$, we need to consider two cases because the absolute value expression can be equal to both the positive and negative of the number inside.

### Case 1: $$ 3x - 5 = 11 $$
$$
\begin{align*}
3x - 5 &= 11 \
3x &= 11 + 5 \
3x &= 16 \
x &= \frac{16}{3}
\end{align*}
$$

### Case 2: $$ 3x - 5 = -11 $$
$$
\begin{align*}
3x - 5 &= -11 \
3x &= -11 + 5 \
3x &= -6 \
x &= -2
\end{align*}
$$

### **Solutions:**
$$
x = \frac{16}{3} \quad \text{and} \quad x = -2
$$

**Answer:**  
$$ \boxed{\dfrac{16}{3}} $$ and $$ \boxed{-2} $$
The solutions are $$ x = \frac{16}{3} $$ and $$ x = -2 $$.

Question 2
Solve the absolute val

and
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Question 2 Solve the absolute val and Submit Question