When we solve inequalities, we are trying to work out what range of values makes the inequality true. One difference in solving these inequalities is that an equals symbol has been replaced by an inequality symbol.

Another difference is that, in an equation such as $x-1=5$x−1=5, only one value of $x$x satisfies the equation. In an inequality such as $x-1>5$x−1>5, there will be many $x$x values that satisfy the inequality.

To solve one-step inequalities, we follow a similar process to one step equations.

Remember

When you multiply or divide by a negative number you have to reverse the inequality sign.

e.g. $-x>3$−x>3 would become $x<-3$x<−3.

Examples

QUESTION 1

Solve the following inequality: $x+5>14$x+5>14

Question 2

Solve the following inequality: $10x<90$10x<90

Question 3

Solve the following inequality: $3x+27>3$3x+27>3

Question 4

Solve the following inequality: $4\left(2x+3\right)>-4$4(2x+3)>−4

Question 5

Solve the following inequality: $2\left(8-\frac{x}{3}\right)\ge14$2(8−x3)≥14 .