Solving Multi Step Equations
If two expressions are equal, then it is called as an equation. when we add, subtract, multiply or divide both sides of the equation with the same number, the equation does not change. If more than two steps are used to solve an equation, it is called as a multi step equation. Now, we are going to see some of the problems on solving multi step equations. In multi-step equations, first we should work on addition and subtraction part and then go for multiplication and division.
Solving Multi Step Equations
Given below are some of the examples in solving multi step equations.
Example 1:
Solve for the variable y in 20 = 3 (2 y + 8) + 4
Solution:
-20 = 3 (2y + 8) + 4
Eliminate the parentheses,
-20 = 3 (2 y) + 3 (8) + 4
-20 = 6 y + 24 + 4
-20 = 6y + 28
Subtract 28 on both sides of the equation
-20 - 28 = 6 y + 28 – 28
-48 = 6 y
Divide by 6 on both sides of the equation
`(-48) / 6` =` (6 y) / 6`
-8 = y
So, the answer is y = -8.
Example 2:
Solve for the variable x: x - 7 = -7x + 81
Solution:
x - 7 = -7x + 81
Add 7 on both sides of the equation
x - 7 + 7 = -7x + 81 + 7
x = -7x + 88
Add 7x on both sides of the equation
x + 7x = -7x + 7x + 88
8x = 88
Divide by 8 on both sides of the equation
`(8x) / 8 = 88 / 8`
x = 11
So, the answer is x = 11.
Practice problems
1) Solve for the variable y: -1y + 45 = y + 65
(Answer: y = -10)
2) Solve for the variable x: 2(x + 1) = 7 + x - 13
(Answer: x = -8)
Solving Multi Step Equations
Given below are some of the examples in solving multi step equations.
Example 1:
Solve for the variable y in 20 = 3 (2 y + 8) + 4
Solution:
-20 = 3 (2y + 8) + 4
Eliminate the parentheses,
-20 = 3 (2 y) + 3 (8) + 4
-20 = 6 y + 24 + 4
-20 = 6y + 28
Subtract 28 on both sides of the equation
-20 - 28 = 6 y + 28 – 28
-48 = 6 y
Divide by 6 on both sides of the equation
`(-48) / 6` =` (6 y) / 6`
-8 = y
So, the answer is y = -8.
Example 2:
Solve for the variable x: x - 7 = -7x + 81
Solution:
x - 7 = -7x + 81
Add 7 on both sides of the equation
x - 7 + 7 = -7x + 81 + 7
x = -7x + 88
Add 7x on both sides of the equation
x + 7x = -7x + 7x + 88
8x = 88
Divide by 8 on both sides of the equation
`(8x) / 8 = 88 / 8`
x = 11
So, the answer is x = 11.
Practice problems
1) Solve for the variable y: -1y + 45 = y + 65
(Answer: y = -10)
2) Solve for the variable x: 2(x + 1) = 7 + x - 13
(Answer: x = -8)