Solve inequalities like equations, reverse the sign when you divide by a negative, show and list the solutions, and describe regions on a graph.
What you will learn
- Solve linear and double inequalities
- Reverse the sign when multiplying or dividing by a negative
- Show inequalities on a number line
- List integer solutions
- Describe a region on a graph with inequalities (Higher)
Solve like an equation
An inequality compares two sides with <, >, ≤ or ≥ instead of =, so its solution is a range of values, such as x < 5.
Most steps are the same as for an equation: 3x + 5 < 20 gives 3x < 15, so x < 5.
The one difference: multiplying or dividing by a negative number reverses the sign. 10 − 2x ≥ 4 gives −2x ≥ −6, so x ≤ 3. (Check: x = 0 works, and 0 ≤ 3.)
With x on both sides, collect as for an equation. 2x + 9 ≥ 6x + 1: subtract 2x, so 9 ≥ 4x + 1, then 8 ≥ 4x, so 2 ≥ x. Read it from the x side: 2 ≥ x is the same as x ≤ 2. An answer can be a fraction: 3x > 2 gives x > 2/3.
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- Solve like an equation
- Integers and problems
- Number lines and integers
- Regions on a graph (Higher)
- Try it: Solve an inequality with the solver
9 practice questions, marked as you go; about 25 minutes in all.
Key terms
Inequality, Negative
In this unit: Linear equations and inequalities
Solve linear equations of every shape, including brackets and fractions, form equations from problems, and solve and show inequalities.