Solving equations and inequalities
in context
e)
h)
10x – 20°
8x
6x + 5°
3d – 11°
47°
1
5x – 20° 7x – 5°
Complete the sentences.
a) Angles on a straight line add up to
b) Angles in a full turn add up to
c) Angles in a triangle add up to
d=
d) Co-interior angles add up to
x=
e) Angles in an n-sided polygon add up to
f)
f) Alternate angles are
i)
3g + 20°
6b
g) Corresponding angles are
h) Vertically opposite angles are
2
2g – 10°
53°
80°
36°
a
a=
b=
Form and solve equations to find the values of the letters.
a)
c)
2x + 30°
3x – 60°
5a + 20°
4b – 12°
160°
g=
x=
b)
5y
g)
b=
d)
6y
y =
a=
j)
3e
2p – 15°
3e
2e
4a
5a – 45°
4a
2e
70°
z
110°
z=
p=
e=
a=
© White Rose Maths 2020
k)
l)
5
3y – 34°
3x – 5°
x + 45°
The area of the rectangle is equal to the area of the parallelogram.
Work out the total area of the two shapes.
6x + 7°
10x – 13°
(x – 2) cm
9 cm
(x + 1) cm
x=
x=
12 cm
y=
3
area =
cm2
A 6-sided dice is biased.
The probability that the dice lands on each number is shown in the table.
Number on dice
1
2
3
4
5
6
Probability
0.1
0.15
x
0.2
2x
0.1
6
(2x + 1) cm
2x cm
7 cm
a) Explain why 2x + 2x + 1 > 7
a) What is the total of the probabilities of the outcomes?
b) Form and solve an equation to find the value of x.
b) Solve the inequality.
x=
c) What is the probability that the dice lands on a number greater than 4?
c) State the smallest possible integer value of x.
7
4
The perimeter of this triangle is 26 cm.
The angles in a triangle are x, 2x and 3x.
Prove that the triangle contains a right angle.
Work out the value of x.
3x cm
(2x + 1) cm
x=
(x + 1) cm
© White Rose Maths 2020