Question

Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.45≥4x+5 and 53>4x+5

Answer 1

Expression given:

$45\ge4x+5$$53>4x+5$

Procedure:

• Solving for ,x ,in first inequality

$-4x\ge-45+5$$-4x\ge-40$$x\le\frac{-40}{-4}$$x\le10$

• Solving for ,x ,in second inequality

$-4x>-53+5$$x<\frac{-48}{-4}$$x<12$

Thus, the graph would be:

If the solution is for both inequalities, then the answer is in which both are included:

$x\le10$