Question

Solve the inequality |2x - 3| ≤ 3 and show your solution on the number line.

Answer 1

Step-by-step explanation:

here

-3< 2x-3<= 3

=> 0< 2x < 6

=> 0< x < 3

so x can take any value which is greater than 0 but is less than 3

hope it helps

Answer 2

The solution of the inequality |2x - 3| ≤ 3 is

x ∈ [0, 3]

Step-by-step explanation:

Given inequality is

$|2x-3|\le3$

Now,

By definition of modulus function we know that

$|2x-3|=-(2x-3)$ for all $x<\frac{3}{2}$

$|2x-3|=(2x-3)$ for all $x\ge\frac{3}{2}$

Case 1

$x<\frac{3}{2}$

$-(2x-3)\le3$

$\implies -2x+3\le3$

$\implies 3-3\le 2x$

$\implies 2x\ge0$

$\implies x\ge 0$

Intersection of $x<\frac{3}{2}$ and $x\ge 0$ is $0\le x<\frac{3}{2}$

or, $x\in [0,\frac{3}{2})$

Case 2

$x\ge\frac{3}{2}$

$(2x-3)\le3$

$\implies 2x-3\le3$

$\implies 2x\le 6$

$\implies x\le\frac{6}{2}$

$\implies x\le 3$

In this case the will be intersection of $x\ge\frac{3}{2}$ and $x\le 3$, which is

$\frac{3}{2}\le x\le 3$

or $x\in [\frac{3}{2}, 3]$

the final solution will be union of $x\in [0.\frac{3}{2})$ and  $x\in [\frac{3}{2},3]$ which is

$x\in[0,3]$

The graph is attached.

Hope this answer is helpful.

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