Solving One and Two Step Equations

Introduction to solving one and two step equations:
Solving one and two step equations is the problems for systems of linear equations. Solving one step equation is the problem that involves the single step of solving the equation and finding the values of the variables. Solving two step equations is the problem that involves the two step of solving the equation and finding the values of the variables.Let us see sample problems for solving one and two step equations.

Solving One and Two Step Equations:

Solving one step equations:

To solve a one-step equation, we must get the variable alone on one side of the equation. This can be done by using inverse operations. Addition and Subtraction (or adding the opposite) are inverse operations. Multiplication and Division are example of inverse operations. Whatever you do to one side of an equation, you must do to the other side (like a balance scale).

Example1:

1) Simplify  `X/5` = 15

`X/5` ·5 = 15 · 5

X = 75

2) Simplify  X – 12 = 18

X – 12 + 12 = 18 +12

X – 12 + 12 = 18 +12

X =30

3)  Simplify   3X =9

`(3X) / X` = 9 /3

`(3X) / X ` = 9 /3

X =3

Example 2:

x +1 = 7  , 1 is being added to the variable, so we must subtract 1 (or add -1) from (to) both sides

x = 6

Example 3:       

6 = y - 5 , 5 is being subtracted from the variable, so we must add 5 to both sides

y =11

Example 4:

y - 1/5 = 1/10 , 1/5 is being subtracted from the variable, so we must add 1/5 to both sides

y = 3/10

Example 5:

-20.2+ 4.1= n - 38.1

n = 22

First we must add -20.2 and 4.1, 38.1 is being subtracted from the variable, so we must add 38.1 to both sides

Example 6:

5 - x =12 , because the 5 is positive, we must subtract 5 (or add -5) to both sides, then the opposite of x is 7, so x is -7

-x = 7

x = -7

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Solving One and Two Step Equations:

Solving Two-Step Equations - Getting variable alone

1. Remove constant by adding opposite to both sides.

2. If variable is being divided by a number, multiply both sides by the number. If variable is being multiplied by a number, divide both sides by the number (remember dividing by a fraction is the same as multiplying by the reciprocal).

Examples:

1) Simplify     `X/3` + 3 = 12

`X/3` + 3 – 3 = 12 – 3

`X/3` + 3 – 3 = 12 – 3

`X/3` = 9

`X/3` = 9

`X/3` · 3 = 9 ·3

X =  `9*3`

X = 27

2) Simplify     4X – 5 = 6

4X – 5 + 5 = 6 + 5

4X – 5 + 5 = 11

4X = 11                  

`(4X)/4` = `11/4`

X = `11/4`

X = 2.75.