Sec 2 Maths · Linear equations, inequalities and simultaneous equations

Solving inequalities questions with answers

Practice questions on solving inequalities, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

Solve $2x + 3 > -3$ .

Step 1 of 2

Collect the x terms on one side and the numbers on the other

2x > -6

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Questions

Question 1ax + b > c
Solve $2x - 1 \geq 5$ .
Show the worked solution
1. Step 1: Collect the x terms on one side and the numbers on the other $2x \geq 6$
2. Step 2: Divide both sides by the number in front of x. Does the sign change? $x \geq 3$
Question 2Negative x term
Solve $-8 - 4x > 4$ .
Show the worked solution
1. Step 1: Collect the x terms on one side and the numbers on the other $-4x > 12$
2. Step 2: Divide both sides by the number in front of x. Does the sign change? $x < -3$ (dividing by a negative number reverses the sign)
Question 3x on both sides
Solve $-3x + 2 < -5x + 1$ .
Show the worked solution
1. Step 1: Collect the x terms on one side and the numbers on the other $2x < -1$
2. Step 2: Divide both sides by the number in front of x. Does the sign change? $x < -\dfrac{1}{2}$
Question 4Fractions
Solve $\dfrac{3x - 3}{2} \geq \dfrac{3x + 3}{3}$ .
Show the worked solution
1. Step 1: Multiply both sides by the LCM of the denominators $3(3x - 3) \geq 2(3x + 3)$
2. Step 2: Expand the brackets $9x - 9 \geq 6x + 6$
3. Step 3: Collect the x terms on one side and the numbers on the other $3x \geq 15$
4. Step 4: Divide both sides by the number in front of x. Does the sign change? $x \geq 5$

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Questions

Question 1ax + b > c

Solve $2x - 1 \geq 5$ .

Show the worked solution

Step 1: Collect the x terms on one side and the numbers on the other $2x \geq 6$
Step 2: Divide both sides by the number in front of x. Does the sign change? $x \geq 3$

Question 2Negative x term

Solve $-8 - 4x > 4$ .

Show the worked solution

Step 1: Collect the x terms on one side and the numbers on the other $-4x > 12$
Step 2: Divide both sides by the number in front of x. Does the sign change? $x < -3$ (dividing by a negative number reverses the sign)

Question 3x on both sides

Solve $-3x + 2 < -5x + 1$ .

Show the worked solution

Step 1: Collect the x terms on one side and the numbers on the other $2x < -1$
Step 2: Divide both sides by the number in front of x. Does the sign change? $x < -\dfrac{1}{2}$

Question 4Fractions

Solve $\dfrac{3x - 3}{2} \geq \dfrac{3x + 3}{3}$ .

Show the worked solution

Step 1: Multiply both sides by the LCM of the denominators $3(3x - 3) \geq 2(3x + 3)$
Step 2: Expand the brackets $9x - 9 \geq 6x + 6$
Step 3: Collect the x terms on one side and the numbers on the other $3x \geq 15$
Step 4: Divide both sides by the number in front of x. Does the sign change? $x \geq 5$