Inequalities

Solve 9 < 2y + 4 < 12

Here is an inequality in y shown on a number line.

Write down the largest possible integer value for y.

On the number line below, show the inequality –4 x < 2

On the grid, show by shading, the region that satisfies all of these inequalities.

Label the region R.

Ron says, “I can remove one of the four inequalities from the grid so that the region R will not change.” Ron is correct.

Which inequality can be removed so that the region R will not change?

21Solve (3x – 1)(5x + 2) < 0

Factorise fully 15w² – 5w

On the number line below, show the set of values of x for which –2 x ≤ 4

On the grid, shade the region R that satisfies all the following inequalities. x ≤ 2 y –3 y ≤ 2x + 1 3x + 2y 6 Label the region R.

16Solve (4x – 3) (x + 5) < 0

Factorise 6x² – 5x – 4

Hence, or otherwise, solve 6x² – 5x – 4 < 0

23Jenna is asked to show the inequality –3 < x ≤ 4 on a number line. Here is her answer.

Write down two mistakes Jenna has made.

Work out the greatest integer that satisfies the inequality

Jenna is asked to show the inequality –3 < x ≤ 4 on a number line. Here is her answer.

Write down two mistakes Jenna has made.

Work out the greatest integer that satisfies the inequality

Find the set of possible values of x for which

You must show all your working.

23–2 ≤ n < 5 n is an integer.

Write down the greatest possible value of n.

On the number line below, show the inequality –4 m < 1

4 –2 ≤ n < 5 n is an integer.

Write down the greatest possible value of n.

On the number line below, show the inequality –4 m < 1

Factorise x² + 10x + 9

The shaded region shown on the grid is bounded by four straight lines.

Find the four inequalities that define the shaded region.

x and y are integers such that 3 < x < 8 4 < y < 10 and x + y = 14 Find all the possible values of x.

23Solve 7x − 27 < 8

Solve 7x − 27 < 8

Find algebraically the set of values of x for which

On the grid show, by shading, the region that satisfies all of these inequalities.

Label the region R.

Write down the inequality shown on this number line.

On the number line below, show the inequality –3 ≤ y 4

Write down the inequality shown on this number line.

On the number line below, show the inequality –3 y 4

Simplify n³ × n⁵

Simplify n³ × n⁵

On the grid show, by shading, the region that satisfies all these inequalities.

Label the region R.

The diagram below shows the region S that satisfies the inequalities

Geoffrey says that the point with coordinates (2, 4) does not satisfy all the inequalities because it does not lie in the shaded region. Is Geoffrey correct? You must give a reason for your answer.

Here is a number line.

Write down the inequality shown on the number line.

The diagram shows a parallelogram.

The area of the parallelogram is greater than 15 cm²

Find the range of possible values of x.

Solve 14 n 11 n + 6

On the number line below, show the set of values of x for which –2 x + 3 4

Solve 14 n 11 n + 6

On the number line below, show the set of values of x for which –2 x + 3 4

Show that (2x + 1)(x 3)(3x + 7) can be written in the form ax³ + bx² + cx d where a, b, c and d are integers.

Show all your working.

On the number line, show the inequality x 4

–5 –4 –3 –2 –1 0 1 2 3 4 5

3 y 7 where y is an integer.

Write down all the possible values of y.

Solve 3x + 5 x + 17

n is an integer such that 3n + 2 14 and 1 Find all the possible values of n.

Here is a rectangle and a right-angled triangle.

All measurements are in centimetres. The area of the rectangle is greater than the area of the triangle.

Find the set of possible values of x.

On the grid, shade the region that satisfies all these inequalities.

Label the region R.

Write down the three inequalities that define the shaded region.

Solve 2x² + 3x – 2