GCSE Secondary Maths Age 13-17 - Algebra: Inequalities - Explained

The video tutorial explains how to solve two inequalities involving an integer N. It covers solving a linear inequality and a quadratic inequality, using a graph to find solutions, and combining these solutions on a number line. The tutorial concludes with advice on tackling similar problems and emphasizes the importance of understanding the methods used.

What is the solution to the linear inequality 3N + 2 ≤ 14?

• N > 4

• N ≤ 4

• N ≥ 4

• N < 4

Why can we multiply both sides of the inequality by n^2 + 5?

• Because n^2 + 5 is always positive

• Because n^2 + 5 is a constant

• Because n^2 + 5 is always negative

• Because n^2 + 5 is zero

What shape does the graph of the quadratic equation n^2 - 6N + 5 form?

• A U-shaped parabola

• An upside-down U-shaped parabola

• A straight line

• A circle

For the quadratic inequality, what are the roots of the equation n^2 - 6N + 5?

• N = 2 and N = 4

• N = 0 and N = 6

• N = 3 and N = 5

• N = 1 and N = 5

What is the range of N for the quadratic inequality n^2 - 6N + 5 < 0?

• N ≥ 0 and N ≤ 6

• N > 0 and N < 6

• N ≥ 1 and N ≤ 5

• N > 1 and N < 5

What is the importance of sketching the graph in solving the quadratic inequality?

• To find the maximum value

• To identify the regions where the inequality holds

• To calculate the exact values of N

• To determine the slope of the line

Which integer values of N satisfy both inequalities?

• 2, 3, 4

• 1, 3, 5

• 1, 2, 3

• 3, 4, 5