Solving equations with variables on both sides worksheets :
Here we are going to see some practice questions on solving equations with variables on both sides.
To solve equations with variables on both sides, we have to bring the variables to the left side of equal sign and the numbers which or not having the variables, that is constants to the right side of equal sign.
(1) Solve the following equation. Then check the solution.
5t - 9 = -3t + 7
(2) Solve the following equation. Then check the solution.
5t - 9 = -3t + 7
(3) Solve the following equation. Then check the solution.
(4) Solve the following equation. Then check the solution.
6(r + 2) - 4 = -10
(5) Solve the following equation. Then check the solution.
4(2a - 1) = -10(a - 5)
(6) Solve the following equation. Then check the solution.
Question 1 :
Solve the following equation. Then check the solution.
5t - 9 = -3t + 7
Solution :
5t - 9 = -3t + 7
In order to get rid of -3t, we have to add 3t on both sides.
5t + 3t - 9 = -3t + 3t + 7
8t - 9 = 7
In order to get rid of -9, add 9 on both sides
8t - 9 + 9 = 7 + 9
8t = 16
Divide by 8 on both sides
8t/8 = 16/8
t = 2
Let us look into the solution of next problem on "Solving equations with variables on both sides worksheets".
Question 2 :
Solve the following equation. Then check the solution.
5t - 9 = -3t + 7
Solution :
5t - 9 = -3t + 7
In order to get rid of -3t, we have to add 3t on both sides.
5t + 3t - 9 = -3t + 3t + 7
8t - 9 = 7
In order to get rid of -9, add 9 on both sides
8t - 9 + 9 = 7 + 9
8t = 16
Divide by 8 on both sides
8t/8 = 16/8
t = 2
L.H.S = 5t - 9 = 5(2) - 9 = 10 - 9 = 1 |
R.H.S = -3t + 7 = -3(2) + 7 = -6 + 7 = 1 |
Hence 2 is the solution.
Question 3 :
Solve the following equation. Then check the solution.
Solution :
(3/4)n + 16 = 2 - (1/8)n
Add (1/8)n on both sides,
(3/4)n + (1/8)n + 16 = 2 - (1/8)n + (1/8)n
(3n/4) + (n/8) + 16 = 2
Subtract 16 on both sides
(3n/4) + (n/8) = 2 - 16
Taking L.C.M on the left side
(3n/4) x (2/2) + (n/8) = -14
(6n/8) + (n/8) = -14
(6n + n)/8 = -14
7n/8 = -14
Multiplying by 8 on both sides
7n = -14(8)
7n = -112
Divide by 7 on both sides
n = -112/7 = -16
L.H.S = (3/4)n + 16 = (3/4) (-16) + 16 = 3 (-4) + 16 = -12 + 16 = 4 |
R.H.S = 2 - (1/8)n = 2 - (1/8) (-16) = 2 + 2 = 4 |
Hence -16 is the solution.
Question 4 :
Solve the following equation. Then check the solution.
6(r + 2) - 4 = -10
Solution :
6(r + 2) - 4 = -10
Use distributive property,
6r + 12 - 4 = -10
6r + 8 = -10
Subtract 8 on both sides,
6r + 8 - 8 = -10 - 8
6r = -18
Divide by 6 on both sides,
6r/6 = -18/6
r = -3
L.H.S = 6(r + 2) - 4 = 6(-3 + 2) - 4 = 6 (-1) - 4 = -6 - 4 = -10 |
R.H.S = -10 |
Hence -1 is the solution.
Question 5 :
Solve the following equation. Then check the solution.
4(2a - 1) = -10(a - 5)
Solution :
4(2a - 1) = -10(a - 5)
Use distributive property,
8a - 4 = -10a + 50
Add 10a on both sides,
8a + 10a - 4 = -10a + 10a + 50
18a - 4 = 50
Add 4 on both sides,
18a - 4 + 4 = 50 + 4
18a = 54
Divide by 18 on both sides,
a = 54/18
a = 3
L.H.S = 4(2a - 1) = 4(2⋅3 - 1) = 4(6 - 1) = 4(5) = 20 |
R.H.S = -10(a - 5) = -10(3 - 5) = -10 (-2) = 20 |
Hence 3 is the solution.
Question 6 :
Solve the following equation. Then check the solution.
5 - (1/2) (x - 6) = 4
Solution :
5 - (x/2) + 6/2 = 4
5 - (x/2) + 3 = 4
By simplifying 5 and 3, we get
8 - (x/2) = 4
Subtract 8 on both sides,
8 - 8 - (x/2) = 4 - 8
-(x/2) = -4
Multiply by -2 on both side,
x = 8
L.H.S = 5 - (1/2) (8 - 6) = 5 - (1/2) (2) = 5 - 1 = 4 |
R.H.S = 4 |
Hence, the solution is 8.
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