Solve $3\left|3\text{x}+2\right|=51$. Check the solution.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

If $x$is a number, then absolute value of $x$is written as $\left|x\right|$.

Here, the inequality is:

$3\left|3x+2\right|=51$

Case 1:

$\begin{array}{c}a=b\\ 3\left(3x+2\right)=51\\ 9x+6=51\\ 9x+6-6=51-6\\ 9x=45\\ x=5\end{array}$

Or Case 2:

localid="1647864878307" $\begin{array}{c}a=-b\\ 3\left(3x+2\right)=-51\\ 9x+6=-51\\ 9x+6-6=-51-6\\ 9x=-57\\ x=-\frac{57}{9}\end{array}$

The solution is localid="1647864888907" $5$and localid="1647864883682" $-\frac{57}{9}$

For case 1: $x=5$.

Check:

localid="1647865021481" $\begin{array}{c}3\left|3x+2\right|=51\\ 3\left|\left(3\times 5\right)+2\right|=51\\ 3\left|15+2\right|=51\\ 3\left|17\right|=51\\ 3\times 17=51\\ 51=51\end{array}$

Thus, it is correct.

For case 2: localid="1647864973875" $x=-\frac{57}{9}$.

Check:

localid="1647865031515" $\begin{array}{r}3\left|3x+2\right|=51\\ 3\left|\left(3\times -\frac{57}{9}\right)+2\right|=51\\ 3\left|-19+2\right|=51\\ 3\left|-17\right|=51\\ 3\times 17=51\\ 51=51\end{array}$

Thus, it is also correct.

Here for localid="1647864903255" $x=-\frac{57}{9}$, the solution is also correct.

Thus $x=5andx=-\frac{57}{9}$are the values of x