Q4. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The value of $\text{x}$ is $5 \mathrm{and} -\frac{57}{9}$.

Step 1 - State the definition of absolute value.

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.

Step 2 - Solve the inequality.

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:

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

The solution is $5$ and $-\frac{57}{9}$

Step 3 - Check the solution.

For case 1: $x=5$.

Check:

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

Thus, it is correct.

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

Check:

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

Thus, it is also correct.

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

Step 4 - State the conclusion.

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