Write down the inequality: x + 5 < 12 Get the x term on its own: x < 7 State the solution: x < 7 Answer: x < 7

Write down the inequality: x - 3 > 4 Get the x term on its own: x > 7 State the solution: x > 7 Answer: x > 7

Write down the inequality: x + 7 ≥ 10 Get the x term on its own: x ≥ 3 State the solution: x ≥ 3 Answer: x ≥ 3

Write down the inequality: x - 6 ≤ 2 Get the x term on its own: x ≤ 8 State the solution: x ≤ 8 Answer: x ≤ 8

Write down the inequality: 3x < 18 Divide both sides by 3: x < 6 State the solution: x < 6 Answer: x < 6

Linear inequalities Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Linear inequalities questions. See exactly how to solve problems on one-step inequality, inverse operations, inclusive inequality, dividing by a positive.

one-step inequalityinverse operationsinclusive inequalitydividing by a positivemultiplying both sidestwo-step inequality

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Solve

x + 5 < 12

Worked solution

Write down the inequality
$x + 5 < 12$
Treat it exactly like an equation, but keep the inequality sign — the aim is to get $x$ on its own.
Get the $x$ term on its own
$x < 7$
Subtract $5$ from both sides — again the sign stays as it is.
State the solution
$x < 7$
This is the complete solution set: every value of $x$ that makes the original inequality true, and no others.

Answer

x < 7

Question 2

1 markeasy

Solve

x - 3 > 4

Worked solution

Write down the inequality
$x - 3 > 4$
Treat it exactly like an equation, but keep the inequality sign — the aim is to get $x$ on its own.
Get the $x$ term on its own
$x > 7$
Add $3$ to both sides — again the sign stays as it is.
State the solution
$x > 7$
This is the complete solution set: every value of $x$ that makes the original inequality true, and no others.

Answer

x > 7

Question 3

1 markeasy

Solve

x + 7 \ge 10

Worked solution

Write down the inequality
$x + 7 \ge 10$
Treat it exactly like an equation, but keep the inequality sign — the aim is to get $x$ on its own.
Get the $x$ term on its own
$x \ge 3$
Subtract $7$ from both sides — again the sign stays as it is.
State the solution
$x \ge 3$
This is the complete solution set: every value of $x$ that makes the original inequality true, and no others.

Answer

x \ge 3

Question 4

1 markeasy

Solve

x - 6 \le 2

Worked solution

Write down the inequality
$x - 6 \le 2$
Treat it exactly like an equation, but keep the inequality sign — the aim is to get $x$ on its own.
Get the $x$ term on its own
$x \le 8$
Add $6$ to both sides — again the sign stays as it is.
State the solution
$x \le 8$
This is the complete solution set: every value of $x$ that makes the original inequality true, and no others.

Answer

x \le 8

Question 5

1 markeasy

Solve

3x < 18

Worked solution

Write down the inequality
$3x < 18$
Treat it exactly like an equation, but keep the inequality sign — the aim is to get $x$ on its own.
Divide both sides by $3$
$x < 6$
Dividing by the positive number $3$ leaves the inequality sign pointing the same way.
State the solution
$x < 6$
This is the complete solution set: every value of $x$ that makes the original inequality true, and no others.

Answer

x < 6

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Linear inequalities Worked Solutions — GCSE Maths

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