Solving Linear Inequalities in GCSE Maths

The video tutorial explains how solving inequalities is similar to solving equations, with the key difference being the sign change when multiplying or dividing by a negative number. It provides examples and strategies to avoid negative multiplication, ensuring the inequality sign remains unchanged. The tutorial includes practice problems to reinforce the concepts.

What is the key difference between solving inequalities and solving equations?

• You must always add to both sides.

• Inequalities cannot be solved.

• The sign flips when multiplying or dividing by a negative number.

• You cannot rearrange inequalities.

In the example problem, what is the first step to isolate x in the inequality 2x + 10 > 12?

• Multiply both sides by 2.

• Subtract 10 from both sides.

• Add 10 to both sides.

• Divide both sides by 2.

After subtracting 10 from both sides in the inequality 2x + 10 > 12, what is the next step?

• Multiply both sides by 2.

• Subtract 2 from both sides.

• Add 2 to both sides.

• Divide both sides by 2.

What is the result of solving the inequality 2x + 10 > 12?

• x > 6

• x < 6

• x = 6

• x ≥ 6

In the alternative method, what is the first step to avoid negative multiplication or division?

• Divide both sides by the smallest x.

• Add the smallest x to both sides.

• Multiply both sides by the smallest x.

• Subtract the smallest x from both sides.

What is the result of solving the inequality 5x - 2x + 23 ≤ 3x + 5?

• x < 6

• x > 6

• x ≥ 6

• x ≤ 6

When solving the inequality -3x + 23 ≤ 5, what happens to the inequality sign when dividing by -3?

• It disappears.

• It becomes an equal sign.

• It flips over.

• It stays the same.

What is the result of solving the inequality -3x + 23 ≤ 5?

• x ≤ -6

• x ≥ -6

• x < -6

• x > -6

In the practice problem, what is the first step to solve 5a < 25?

• Multiply both sides by 5.

• Divide both sides by 5.

• Subtract 3 from both sides.

• Add 3 to both sides.

What is the result of solving the inequality 5a < 25?

• a > 5

• a < 5

• a = 5

• a ≤ 5