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Middle Years

7.02 Solutions to equations

Worksheet
Substitution
1

For each of the following equations, state whether the given value of x is the solution:

a

17 + x = 40, \enspace x = 20

b

32 + x = 58, \enspace x = 26

c

2 x = 10, \enspace x = 5

d

\dfrac{x}{9} = 8, \enspace x = 71

e

\dfrac{x}{10} = 6, \enspace x = 60

f

8 - x = 10, \enspace x = 2

g

4 x = -12, \enspace x = -3

h

x - 30 = 21, \enspace x = 48

i

x - 18 = 14, \enspace x = 32

j

7 x = 33, \enspace x = 5

k

\dfrac{x}{4} = -4, \enspace x = 16

l

\dfrac{x}{20} = 5, \enspace x = 100

2

For each of the following, state whether the given value of the pronumeral is the solution of the equation:

a
u + 33 = 48, \enspace u = 22
b
v + 27 = 63,\enspace v = 27
c
t - 32 = 31,\enspace t = 57
d
48 - v = 11,\enspace v = 37
e
7 r = 63,\enspace r = 11
f
\dfrac{v}{9} = 11,\enspace v = 99
3

Determine whether the following equations have p = 8 as a solution:

a
35 - p = 27
b
\dfrac{50}{p} = 6
c
6 p = 48
d
23 + p = 31
e
26 - p = 23
f
29 + p = 35
g
10 + p = 28
h
\dfrac{80}{p} = 10
i
11 p = 96
j
p -14 = 6
k
p - 11 = -3
l
24 + p = 34
4

Determine whether the following equations have r = 48 as a solution:

a
2 r = 93
b
r + 12 = 60
c
r - 15 = 33
d
\dfrac{r}{6} = 8
e
\dfrac{r}{6} = 5
f
17 + r = 65
g
3 r = 134
h
r + 25 = 73
i
95 - r = 47
j
\dfrac{r}{4} = 22
k
\dfrac{96}{r} = 2
l
28 + r = 76
5

Determine whether the following equations have y = 8 as a solution:

a
5 y = 40
b
23 + y = 25
c
22 - y = 18
d
\dfrac{y}{4} = 2
e
4 y = 29
f
45 - y = 32
g
8 y = 64
h
y+35 = 45
i
56 - y = 38
j
\dfrac{40}{y} = 5
k
3 y = 16
l
y - 3 = 5
6

Which of the following is the solution to the equation x-10 = 30?

A
20
B
40
C
3
D
300
Trial and error
7

Consider the equation 56 - t = 39.

a

Which side of the equation is bigger when substituting t = 10?

b

Should we try a smaller or larger number than 10 to solve the equation?

c

Which side of the equation is bigger when substituting t = 20.

d

Hence, what can be said about the solution of the equation?

8

Consider the equation 2 u = 70.

a

Which side of the equation is bigger when substituting u = 30?

b

Should we try a smaller or larger number than 30 to solve the equation?

c

Which side of the equation is bigger when substituting u = 40?

d

Hence, what can be said about the solution of the equation?

9

Consider the equation m - 17 = 12.

a

Complete the table:

\enspace m252627282930
m-17
b

Hence, what value of m will make the equation true?

10

Consider the equation 4k = 96.

a

Complete the table:

\enspace k202122232425
4k
b

Hence, what value of k will make the equation true?

11

Use trial and error to find the solution of each of the following equations:

a
47 - t = 14
b
3 v = 72
c
y + 20 = 36
d
x + 24 = 43
e
t + 19 = 35
f
s + 12 = 38
g
n - 16 = 8
h
5 j = 120
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