Inequalities

Write down the inequality shown on the number line.

Solve the inequality 7a 5 3a 28 Show clear algebraic working.

Write down the inequality shown on the number line.

Solve the inequality 7a 5 3a 28 Show clear algebraic working.

Lui is asked to work out the value of 30 – 4 x when x = –5

Here is his working and his answer.

Lui’s answer is wrong.

Explain what Lui has done wrong in his working.

Oni thinks of a number. She calls the number Y

Y is a positive, odd number and Y 9

Write down all the possible values of Y

Solve the inequality 7 – 3t < 2t + 15

The region R, shown shaded in the diagram, is bounded by three straight lines.

Write down three inequalities that define the region R

Solve the inequality 7 – 3t < 2t + 15

The region R, shown shaded in the diagram, is bounded by three straight lines.

Write down three inequalities that define the region R

19Solve the inequality 4x² 4x 15 0 Show clear algebraic working.

Factorise x² 5x 24

Hence, solve x² 5x 24 0

Solve the inequality 3y 5 7y 10

Show clear algebraic working.

Simplify g⁹ g²

Expand 5k²(k³ + 4)

Factorise x² 2x 63

Hence, solve x² 2x 63 = 0

Solve the inequality 7 2y 3y 12

Simplify g⁹ g²

Expand 5k²(k³ + 4)

Factorise x² 2x 63

Hence, solve x² 2x 63 = 0

Solve the inequality 7 2y 3y 12

Solve the inequality 8x 4 3x 10

The region R, shown shaded in the diagram, is bounded by three straight lines.

Write down the three inequalities that define the region R

Expand x (x + 3)

Factorise 8p + 10

Make e the subject of y = eh ‒ f

Janya thinks of a whole number. She calls her whole number w Janya writes down this information about her whole number.

Write down the possible values of w

The region R, shown shaded in the diagram, is bounded by three straight lines.

Find the inequalities that define R

The region R, shown shaded in the diagram, is bounded by three straight lines.

Find the inequalities that define R

Factorise y² – 2y – 48

Write down the inequality shown on the number line

–2 –1 0 1 2 3 4 5

Solve the inequality 7w + 6 12w + 14

Some members of a library were asked to name the type of book that they each liked to read the best.

One of the members is chosen at random. The table shows information about the probability of the type of book that this member answered.

48 members answered comedy books.

Work out how many of the members answered mystery books.

Factorise y² – 2y – 48

Write down the inequality shown on the number line

–2 –1 0 1 2 3 4 5

Solve the inequality 7w + 6 12w + 14

The region R, shown shaded in the diagram, is bounded by the straight lines with equations

2x + y = 6

2y = 5x + 1

3y + 2x = 4

Write down the three inequalities that define R

The table gives information about the costs of sending parcels of different weights.

Weight (wkg)	Cost of sending a parcel
0 w 1	£6.00
1 w 2	£9.02
2 w 5	£15.85
5 w 10	£21.90

Peony has one parcel of weight 1.3 kg and another parcel of weight 8 kg to send to two different places.

Work out the total cost of sending these two parcels.

Gryffyn sends 3 parcels each to a different place. One of the parcels has a weight of 1.5 kg and another of the parcels has a weight of 2.8 kg The total cost of sending the 3 parcels is £33.89

Work out the greatest possible weight of the third parcel.

–8 < 2y ≤ 2 y is an integer.

Find all the possible values of y

Write down the inequality shown on the number line.

–5 –4 –3 –2 –1 0 1 2 3 4 5

3 –8 < 2y ≤ 2 y is an integer.

Find all the possible values of y

Write down the inequality shown on the number line.

–5 –4 –3 –2 –1 0 1 2 3 4 5

22Solve the inequality 6x² + 37x 35 Show clear algebraic working.

Solve the inequality 3 – 4x ≤ 11

19f(x) = x² – 4

g(x) = 2x + 1

Solve fg(x) 0 Show clear algebraic working.

n is an integer.

Write down all the values of n such that –2 n < 3

On the number line, represent the inequalityy 1

–3 –2 –1 0 1 2 3

Solve the inequality 5x – 7 ≤ 2

Factorise y² – 2y – 35

Hence, solve y² – 2y – 35 = 0

Solve the inequality 5x – 7 ≤ 2

Factorise y² – 2y – 35

Hence, solve y² – 2y – 35 = 0

Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5)

Show, by shading on the grid, the region defined by all three of the inequalities

Label the region R

Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5)

Show, by shading on the grid, the region defined by all three of the inequalities

Label the region R

The shaded region in the diagram is bounded by three lines. The equation of one of the lines is given.

Write down three inequalities that define the shaded region.

Here is a rectangle.

(2 x + 3) cm
Diagram NOT

Given that the area of the rectangle is less than 75 cm²

find the range of possible values of x

Solve the inequalities –7 ≤ 2x – 3 5

On the number line, represent the solution set to part (i)

Solve the inequalities –7 ≤ 2x – 3 5

On the number line, represent the solution set to part (i)

On the number line, show the inequality –2 ≤ y < 1

–3 –2 –1 0 1 2 3

n is an integer.

Write down all the values of n that satisfy –3.4 < n 2

On the number line, show the inequality –2 y < 1

–3 –2 –1 0 1 2 3

n is an integer.

Write down all the values of n that satisfy –3.4 n ≤ 2

On the grid, draw and label the straight line with equation

x = 1.5

y = x

x + y = 6

Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.

Expand and simplify 4 x (2 x + 5) – 3 x (2 x – 3)

work out the value of n.

Solve the inequality 7t – 8 < 2t + 7

On the number line below, represent the solution set of the inequality solved in part (c)(i)

–5 –4 –3 –2 –1 0 1 2 3 4 5

The shaded region R, shown in the diagram below, is bounded by the straight line with equation y = 3 x – 2 and by two other straight lines.

Write down the three inequalities that define region R.

Factorise 25 f – 10

Make y the subject of the formula c = 5y – h

Solve the inequality 4x + 7 > 2

Factorise x² – x – 42

Solve the inequality 3x + 15 < 8x + 3

Show clear algebraic working.

Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.

Simplify g⁶ g⁴

Simplify k¹⁰ ÷ k³

Simplify (3cd⁴)²

Solve the inequality 4x + 7 > 2

The diagram shows a rectangle.

The area of the rectangle is Acm²

Given that A 3x + 27 find the range of possible values for x.

21The function f is such that f(x) = 5 + 6x – x²for x ≤ 3

Express 5 + 6x – x² in the form p – (x – q)² where p and q are constants.

Using your answer to part (a), find the range of values of x for which f^–1(x) is positive.

The shaded region in the diagram is bounded by three lines. The equation of one of the lines is given.

Write down the three inequalities that define the shaded region.

Here are five mathematical signs

Write one of these five signs in each box so that each of these statements is true.

The table gives information about the boiling points and the freezing points of some elements.

Which of these elements has the lowest boiling point?

Which of these elements has the largest difference in temperature between its boiling point and its freezing point?

Dr Strauss is going to cool chlorine from its boiling point to its freezing point. He knows that it will take 2 minutes for the temperature of the chlorine to go down 10C.

Work out how long it will take the chlorine to cool from its boiling point to its freezing point?

Solve the inequality 2x + 7 4

Solve x² – 3x – 40 = 0 Show clear algebraic working.

Write down the integer values of x that satisfy the inequality −2 x ≤4

The region R, shown shaded in the diagram, is bounded by three straight lines.

Write down the three inequalities that define the region R.

Write down the integer values of x that satisfy the inequality –2 x 4

The region R, shown shaded in the diagram, is bounded by three straight lines.

Write down the three inequalities that define the region R.

Show clear algebraic working.

Solve the inequality 5y² – 17y 40

Write down the inequality shown on the number line.

Solve the inequality 4y≤ y + 8

The straight line L has gradient 5 and passes through the point with coordinates (0, í3)

Write down an equation for L.

The region R, shown shaded in the diagram, is bounded by four straight lines.

Write down the inequalities that define R.

On the grid, draw the graph of y = 2 x + 3 for values of x from í2 to 3

Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.

The diagram shows two straight lines drawn on a grid.

Write down the solution of the simultaneous equations

3 y = 2 x + 6 4 x + 3 y = 24

Show, by shading on the grid, the region defined by all five of the inequalities

Label the region R.

Here is a sequence of patterns made from dots.

Pattern Pattern Pattern Pattern number 1 number 2 number 3 number 4

Draw Pattern number 4 in the space above.

Complete the table.

Work out the number of dots in Pattern number 13

Find an expression, in terms of n, for the number of dots in Pattern number n.

There are fewer than 90 dots in Pattern number k.

What is the largest possible value of k ?

Make a the subject of the formula M = ac – bd

Solve the inequality 5x – 4 39

Factorise fully 18e²f³ – 12e³ f

Make a the subject of the formula M = ac – bd

Solve the inequality 5x – 4 39

Factorise fully 18e²f³ – 12e³ f

Solve the inequality 4x² – 5x – 6 0