Inequalities

Write down the inequality shown on this number line.

Solve.

2 x - 1 ⩽ 11

Solve.

4 x ⩽ 20

Show your solution to part (a) on the number line.

For each statement, tick (✓) whether the value of x is true or false. The first one is done for you.

In the diagram below, the shaded region is a parallelogram. The parallelogram can be identified by four inequalities. Two of the inequalities are y ⩾ 6 and y ⩾ x.

Write down the other two inequalities that identify the parallelogram.

Work out the area of the parallelogram. You must show your working.

(b)........ square units

Solve 7 x - 3 < 11.

Show your solution on the number line.

Use one of these symbols <, > or = to make each statement true.

60 mm........ 6 cm

320 g........ 3.2 kg

Solve the inequality.

x² - 100 ⩾ 0.

The region R is shown on this grid.

The region R is defined by three inequalities. The first inequality is given below.

Complete the second inequality and write down the third inequality needed to define region R.

y ⩾ 0

2 y........ 3 x + 6

Multiply out.

5 a (2 - a)

Solve.

5 x + 9 > 12

Solve by factorising.

x² + 7x + 12 = 0

Find all the possible integer values that satisfy the inequality - 10 < 3 x + 2 ⩽ 8.

The graph of y = x is drawn on the grid.

The region R satisfies the following inequalities.

y ⩾ x y ⩽ 2 y < - 2 x - 3

By drawing two more straight lines on the grid, find and label the region R.

Show the inequality x > -2 on this number line.

The graphs of x = - 3 and y = - x are drawn on the grid.

The region R satisfies the following inequalities.

By drawing one more line, find and label the region R.

Use one of these symbols <, = or > to make each statement true.

4²........ 9

Find all the possible integer values that satisfy the inequality 4 ⩽ 2 x < 10.

Find all the possible integer values that satisfy the inequality - 4 ⩽ x - 3 < 1.

The region R is shown on this grid. A is the point (0, 3) and B is the point (3, 4.5).

Show that an equation of the straight line through A and B is 2 y = x + 6.

Write down the three inequalities that define region R.

Solve 2 x + 5 ⩾ 11. Show your solution on the number line.

1 2 3 4 5 6 7 8 9

Solve this inequality.

x² + 4x - 12 ⩽ 0

Give your answer using set notation. You must show your working.

The graph of y = 2 x + 1 is drawn on this one centimetre grid.

The region R satisfies these inequalities.

y ⩽ 2 x + 1 y ⩾ 5 x + y ⩽ 13

Show that the area of region R is 12 cm².

Solve the inequality.

2 (x + 5) < 16

The region R is shown on this grid.

Region R is defined by four inequalities. One of the inequalities is x ⩾ 0.

Use the symbols ⩽ and ⩾ to complete the other three inequalities.

x ⩾ 0

x + 2 y........ 24

The inequality x ⩾ 0 is replaced by a new inequality. Region R is then a kite.

Write down the new inequality.

Solve the inequality.

4 (x - 3) < x

Show your answer to part (a) on the number line.

Solve 3 x + 4 < 19. Show your solution on the number line.

The graphs of y = x and y = - 2 are drawn on the grid.

The region R satisfies the following inequalities.

y ⩾ - 2 y ⩽ x y < 4 - 2 x

By drawing one more line, find and label the region R.

Solve 3 x + 4 < 19. Show your solution on the number line.

Write down the inequality shown on this number line.

Solve 3 x - 5 ⩾ 10. Show your solution on the number line.

1 2 3 4 5 6 7

Solve 3 x - 5 ⩾ 10. Show your solution on the number line.

1 2 3 4 5 6 7

Region R satisfies these inequalities.

y > 3 y ⩾ x x + y ⩽ 9

By drawing three straight lines on the grid, find and label the region R.

Martha’s solution to the inequality 8 x + 5 ⩽ 3 x - 10 is shown on the number line.

Is her solution correct? Explain your reasoning.

Show the inequality x > 3 on this number line.

Simplify.

4 a + 3 c + 7 a - 5 c

Solve.

The diagram shows the lines y = 2 x + 1 and 7 x + 4 y = 28.

The region R satisfies these inequalities.

y ⩽ 2 x + 1 7 x + 4 y ⩾ 28
y > 1

By drawing a third straight line, find and label the region R that satisfies these inequalities.

Multiply out.

4 c (d – 5)

Multiply out and simplify.

(3 x + 2)(x – 4)

Solve.

3 x - 2 ⩽ 22

Write down.

3091 rounded to the nearest hundred

3% as a decimal

the cube root of 27

Complete the statement below using a number from this list.

- 2 0 - 6 6

Write the following numbers in order of size, smallest first.

0.4 0.5 0.06 0.444 0.46

smallest

Gemma’s solution to the inequality 3 x + 1 > – 5 is shown on the number line.

Is Gemma’s solution correct? Explain your reasoning.

Use one of these symbols <, > or = to make each statement true.

6........ 2³

Write down the inequality for x that is shown on this number line.

Solve the inequality.

The diagram below shows a 1 cm coordinate grid.

Find an inequality that defines region A and another inequality that defines region B.

Shade the region on the grid given by the inequality y ⩾ 6.

A fourth shaded region, given by the inequality

y ⩾ kx + 2,

is added to the grid.

The unshaded region now has area 23 cm².

Find the value of k.

Solve the inequality.

3 x - 2 > 10

Solve.

6 x + 2 = 5 - 4 x