Question

If $5x-3\le 5+3x\le 4x+2$, express it as $a\le x\le b$.

• A. $-3\le x\le 4$
• B. $3\le x\le -4$
• C. $3\le x\le 4$
• D. $-3\le x\le 3$

Answer 1

The correct option is C $3\le x\le 4$

Given: $5x-3\le 5+3x\le 4x+2$

$\Rightarrow 5x-3\le 5+3x\le 4x+2$

$\Rightarrow 5x-3\le 5+3x\text{and}5+3x\le 4x+2$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequations.
$\Rightarrow 5x-3x\le 5+3\text{and}5-2\le 4x-3x$

$\Rightarrow 2x\le 8and3\le x$

$\Rightarrow x\le 4andx\ge 3$

Therefore,

$a\le x\le b\Rightarrow 3\le x\le 4$