Solve inequalities instead of equations, and learn the one crucial rule that's different from solving equations.
Inequalities are solved almost exactly like equations, adding or subtracting the same amount from both sides. The key difference: if you multiply or divide both sides by a negative number, the inequality sign must flip direction.
Solve: x + 4 > 9
x > 5
Solve: −2x < 8
Dividing by −2 flips the sign: x > −4
A solution like x > 5 is shown on a number line with an open circle at 5 (since 5 itself isn't included) and shading to the right. A solution like x ≤ 5 uses a filled circle, since 5 is included.
How would you represent x > 3 on a number line?
An open circle at 3, with shading extending to the right
How would you represent x ≤ −2 on a number line?
A filled circle at −2, with shading extending to the left
1. Solve: x − 5 < 3
2. Solve: 3x + 2 ≥ 14
3. Solve: −4x > 12
4. How would you represent x < 6 on a number line?
5. Solve: 2x − 7 ≤ 5