Two Step Equations Variables on Both Sides Worksheet Easy
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES WORKSHEET
Question 1 :
Solve for t :
5t - 9 = -3t + 7
Question 2 :
Solve for n :
3n/4 + 16 = 2 - n/8
Question 3 :
Solve for n :
4(2a - 1) = -10(a - 5)
Question 4 :
Solve for x :
-7x - 3x + 2 = -8x - 8
Question 5 :
Solve for k :
5(k - 3) - 7(6 - k) = 24 - 3(8 - k) - 3
Question 6 :
Solve for x :
(x + 15)(x - 3) - (x2 - 6x + 9) = 30 - 15(x - 1)
Question 7 :
Solve for x :
4x/5 - 7/4 = x/5 + x/4
Question 8 :
Solve for x :
(x - 2)/2 + (x + 10)/9 = 5
Question 9 :
Solve the following equation :
(1/2)(8y - 6) = 5y - (y + 3)
Question 10 :
Solve the following equation :
2(1 - x) + 5x = 3(x + 1)
Detailed Answer Key
Question 1 :
Solve for t :
5t - 9 = -3t + 7
Solution :
5t - 9 = -3t + 7
Add 3t to each side.
8t - 9 = 7
Add 9 to each side.
8t = 16
Divide each side by 8.
t = 2
Question 2 :
Solve for n :
3n/4 + 16 = 2 - n/8
Solution :
3n/4 + 16 = 2 - n/8
Least common multiple of the denominators (4 and 8) is 8.
Multiply each side by 8 to get rid of the denominators 4 and 8.
8[3n/4 + 16] = 8[2 - n/8]
Use the distributive property.
8(3n/4) + 8(16) = 8(2) - 8(n/8)
6n + 128 = 16 - n
Add n to each side.
7n + 128 = 16
Subtract 128 from each side.
7n = -112
Divide each side by 7.
n = -16
Question 3 :
Solve for n :
4(2a - 1) = -10(a - 5)
Solution :
4(2a - 1) = -10(a - 5)
Use the distributive property.
4(2a) - 4(1) = -10(a) - 10(-5)
8a - 4 = -10a + 50
Add 10a to each side.
18a - 4 = 50
Add 4 to each side.
18a = 54
Divide each side by 18.
a = 3
Question 4 :
Solve for x :
-7x - 3x + 2 = -8x - 8
Solution :
-7x - 3x + 2 = -8x - 8
Simplify.
-10x + 2 = -8x - 8
Add 10x to each side.
2 = 2x - 8
Add 8 to each side.
10 = 2x
Divide each side by 2.
5 = x
Question 5 :
Solve for k :
5(k - 3) - 7(6 - k) = 24 - 3(8 - k) - 3
Solution :
5(k - 3) - 7(6 - k) = 24 - 3(8 - k) - 3
Use distributive property.
5k - 15 - 42 + 7k = 24 - 24 + 3k - 3
Simplify.
12k - 57 = 3k - 3
Subtract 3k from each side.
9k - 57 = -3
Add 57 to each side.
9k = 54
Divide each side by 9.
k = 6
Question 6 :
Solve for x :
(x + 15)(x - 3) - (x2 - 6x + 9) = 30 - 15(x - 1)
Solution :
(x + 15)(x - 3) - (x 2 - 6x + 9) = 30 - 15(x - 1)
Simplify.
x2 + 12x - 45 - x2 + 6x - 9 = 30 - 15x + 15
18x - 54 = -15x + 45
Add 15x to each side.
33x - 54 = 45
Add 54 to each side.
33x = 99
Divide each side by 33.
x = 3
Question 7 :
Solve for x :
4x/5 - 7/4 = x/5 + x/4
Solution :
4x/5 - 7/4 = x/5 + x/4
The least common multiple of the denominators (4 and 5) is 20.
Multiply each side by 20 to get rid of the denominators 4 and 8.
20[4x/5 - 7/4] = 20[x/5 + x/4]
20(4x/5) - 20(7/4) = 20(x/5) + 20(x/4)
16x - 35 = 4x + 5x
16x - 35 = 9x
Subtract 9x from each side.
7x - 35 = 0
Add 35 to each side.
7x = 35
Divide each side by 7.
x = 5
Question 8 :
Solve for x :
(x - 2)/2 + (x + 10)/9 = 5
Solution :
(x - 2)/2 + (x + 10)/9 = 5
The least common multiple of the denominators (2 and 9) is 18.
Multiply each side 18 to get rid of the denominators 2 and 9.
18[(x - 2)/2 + (x + 10)/9] = 18(5)
18(x - 2)/2 + 18(x + 10)/9 = 90
9(x - 2) + 2(x + 10) = 90
9x - 18 + 2x + 20 = 90
11x + 2 = 90
Subtract 2 from each side.
11x = 88
Divide each side by 11.
x = 8
Question 9 :
Solve the following equation :
(1/2)(8y - 6) = 5y - (y + 3)
Solution :
(1/2)(8y - 6) = 5y - (y + 3)
Simplify both sides.
4y - 3 = 5y - y - 3
4y - 3 = 4y - 3
Subtract 4y from each side.
-3 = -3
The above result is true. Because the result we get at the last step is true, the given equation has infinitely has many solutions.
Question 10 :
Solve the following equation :
2(1 - x) + 5x = 3(x + 1)
Solution :
2(1 - x) + 5x = 3(x + 1)
Simplify both sides.
2 - 2x + 5x = 3x + 3
2 + 3x = 3x + 3
Subtract 3x from each side.
2 = 3
The above result is false. Because 2 is not equal to 3. Because the result we get at the last step is false, the given equation has no solution.
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