Answer
.
Work Step by Step
First, simplify the above expression.
Then divide the above expression by 3:
$\frac{3\left| 2x-1 \right|}{3}\ge \frac{21}{3}$
Further, the above expression becomes
$\left| 2x-1 \right|\ge 7$
So the absolute value or modulus function is denoted by $\left| x \right|.$ Here, x is a real number and the absolute value or modulus function of x is defined as $\left| x \right|=\left\{ \begin{align}
& \,\,\,x,\,x\ge 0 \\
& -x,\,x<0 \\
\end{align} \right.$
So,
$\left| 2x-1 \right|=\left( 2x-1 \right)$ or $\left| 2x-1 \right|=-\left( 2x-1 \right)$
As $\left| 2x-1 \right|\ge 7,$
$\left( 2x-1 \right)\ge 7$ or $-\left( 2x-1 \right)\ge 7$
Now solve the above inequality:
$\left( 2x-1 \right)\ge 7$
Add 1 to both sides of the above inequality:
$2x\ge 8$
Divide both sides of the above inequality by 2:
So, $x\ge 4.$
Now, solve the inequality $-\left( 2x-1 \right)\ge 7$:
$-2x+1\ge 7$
Subtract 1 from both sides of the above equation:
$-2x\ge 6$
Divide both sides of the above inequality by −2:
When the inequality is multiplied or divided by a negative number, the sign of inequality gets reversed.
So, $x\le -3.$
The solution set is $\left\{ x|-3\ge x\ge 4 \right\}$ of the inequality $3\left| 2x-1 \right|\ge 21$.
