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(-40)/(-4)`
`x\le10`

• Solving for ,x ,in second inequality

`-4x>-53+5`
`x<(-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`