Simplify
Brackets
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Problems
100
5h + 2 + 2h = 23
7h + 2 = 23
7h = 21
h = 3
100
2(x + 5) = 14
2x+ 10 = 14
2x = 4
x = 2
100
2x + 5 = 3x - 1
5 = x - 1
x = 6
100
4x + 9 = 33
4x = 24
x = 6
100
WRITE AN EQUATION & SOLVE:
Julie is 3 years older than her sister.
Julie is 11 years old.
How old is her sister?
Let n be Julie's sister's age, so
n + 3 = 11
n = 8
Julie's sister is 8 years old.
200
3b + b - 8 = 4
4b - 8 = 4
4b = 12
b = 3
200
5(d - 2) = 40
5d - 10 = 40
5d = 50
d = 10
200
5x + 5 = 7x - 4
5 = 2x - 4
9 = 2x
x = 4.5
200
x + 3x = -8
4x = -8
x = -2
200
The angles in a triangle are given as 3a, 5a and 4a.
What are their sizes?
3a + 5a + 4a = 180
12a = 180
a = 15
So the angle sizes are 450, 750 and 600.
300
3a + 12 - 6a = -9
-3a + 12 = -9
-3a = -21
a = 7
300
7(4 - t) = -84
28 - 7t = -84
-7t = -112
t = 16
300
3(y + 6) = 5y + 12
3y + 18 = 5y + 12
18 = 2y + 12
6 = 2y
y = 3
300
4(y - 2) + y = -13
4y - 8 + y = -13
5y - 8 = -13
5y = -5
y = -1
300
Find the size of these angles.
3y + 20 = 5y - 20
20 = 2y - 20
40 = 2y
y = 20
Angles = 800 each
400
-6 = -3y + 4 + 5y
2y + 4 = -6
2y = -10
y = -5
400
-2(x - 9) = -24
-2x + 18 = -24
-2x = -42
x = 21
400
5(y + 6) = 3(y + 12)
5y + 30 = 3y + 36
2y + 30 = 36
2y = 6
y = 3
400
-6(m + 1) + 18 = 24
-6m - 6 + 18 = 24
-6m + 12 = 24
-6m = 12
m = -2
400
Theatre tickets for 2 adults and 1 senior citizen cost a total of £31. A senior citizen ticket costs £5 less than an adult ticket. Work out the cost of an adult ticket.
Let t be the cost of an adult ticket. So a senior citizen ticket would be t - 5.
So, 2t + t - 5 = 31
3t - 5 = 31
3t = 36
t = 12, so an adult ticket is £12.
500
78 = 3c + 12 - c + 4
2c + 16 = 78
2c = 62
c = 31
500
-13(4 + 2a) = 208
-52 - 26a = 208
-26a = 260
a = -10
500
6(x - 5) = 3(x - 2)
6x - 30 = 3x - 6
3x - 30 = -6
3x = 24
x = 8
500
7k - 8 + 2(k + 12) = 52
7k - 8 + 2k + 24 = 52
9k + 16 = 52
9k = 36
k = 4
500
When you count up in ones from any integer, you are counting consecutive integers. Using algebra, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?
n + n + 1 + n + 2 = 48
3n + 3 = 48
n = 15
The integers are 15, 16, and 17.