Question

What is the solution to the compound inequality 3x − 8 ≥ −5 and 2x − 7 < 5?

Answer 1

Answer:

The solution to the compound inequality is given by:

                       $1\leq x$

Step-by-step explanation:

The compound inequality is given by:

$3x-8\geq -5$ and

$2x-7$

• On solving the first inequality i.e.

$3x-8\geq -5$

on adding both side of the inequality by 8 we get:

$3x\geq -5+8\\\\i.e.\\\\3x\geq 3$

Now on dividing both side of the inequality by 3 we get:

$x\geq 1$

• The second inequality is given by:

$2x-7$

On adding both side of the inequality by 7 we get:

$2x$

on dividing both side of the inequality by 2 we get:

$x$

Hence, the solution of the compound inequality is:

                    $1\leq x$

Answer 2

1<x<6 or its x>1 and x>6