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# Solving Two-Step Equations – Techniques & Examples** **

## What is a Two-step Equation?

It is probably undebatable that a two-step equation is as easy as ABC. As the name suggests, a two-step equation is an algebraic equation which requires only two steps to be completely solved.

The equation is already solved when the value of the variable is found. In this article, we are going take you **step by step in solving two-step equations** so to make you familiar and proficient with the process.

Generally, when solving an equation, we apply the Law of Equations which states that whatever that is to be performed on the right-hand side (RHS) of an equation should also be done to the left-hand side (LHS) of the equation so that the equation can remain balanced.

A **two-step equation** is said have been solved if a variable, usually represented by an alphabetical letter is isolated on either the left or right side of the equation and the number is located on the opposite side.

## How to Solve Two-step Equations?

Solving a two-step equation involves working backwards with respect to the order of operations (PEMDAS). In this case, multiplication and division is preceded by addition and subtraction.

**Tips for Solving Two-step equations include:**

- Always apply addition or subtraction to remove a constant.
- Apply multiplication or division to remove any coefficient from a variable.

*Example 1*

Solve the two-step equation y:

3y – 2 = 13

__Solution__

Add 2 to both sides of the equation and divide by 3.

3y – 2 + 2 = 13 + 2

3y = 15

3y/3 = 15/3

y = 5

*Example 2*

Solve the two-step equation for z.

2z +15 = −3z

__Solution__

Subtract 2z from both sides of the equation and divide by -5.

2z – 2z + 15 = -3z – 2z

15 = -5z

15/-5 = -5z/-5

z = 3

*Example 3*

Solve the two-step equation for x

(x/5) -6 = -8

__Solution__

Add both 6 to both sides of the equation and multiply by 5.

(x/5) – 6 + 6 = – 8 + 6

(x/5)5 = – 2 x 5

x = -10

*Example 4*

Solve the two-step equation for k.

(k + 5)/2 = 8

__Solution__

Multiply 2 on both sides of the equation then, subtract 5 from both sides as well.

2 x (k + 5)/2 = 8 x 2

k + 5-5 = 16 -5

k = 11

*Example 5*

Solve the two-step equation for y.

5y/4 + 2y/3 = 5

__Solution__

Multiply each term of the equation by the LCD.

The LCD = 12

(5y/4)12 + (2y/3)12 = 5 x 12

15y + 8y = 60

23y = 60

23y/23 = 60/23

y = 60/23

*Example 6*

Solve the equation for x in the following two step equation.

4.25 – 0.25x = 3.75

__Solution__

Subtract 4.25 from both sides and divide by – 0.25

4.25 – 4.25- 0.25x = 3.75 – 4.25

– 0.25x = – 0.5

-0.25x/-0.25 = – 0.5/- 0.25

X = 2

*Example 7*

Solve for x in the two-step equation 5x − 6 = 9

__Solution__

Add 6 to both sides.

5x – 6 + 6 = 9 + 6

5x = 15

Divide both sides by.

5 x /5 = 15/5

x = 3

*Example 8*

Solve for x in the equation -2x – 3 = 4x – 15.

__Solution__

Adding +3 to the left and right side of the equation will give;

(-2x – 3) +3 = (4x – 15) +3 = -2x = 4x – 12

Subtract -4x from both sides of the equation.

-2x – 4x = (4x – 12) – 4x = -6x = -12

Divide both sides of the equation by -6.

-6x ÷ -6 = -12 ÷ -6

x = 2

*Example 9*

Solve for x in the two-step equation:4x + 7 – 6 = 5 – 4x + 4

__Solution__

First simplify both sides of the equation by combining like terms.

4x + 1 = 9 – 4x.

Add 4x and subtract 1 from both sides of the equation.

8x = 8.

Divide both sides the equation by 8.

8x /8 = 8/8

x = 1

*Example 10*

Solve for x in the following two step equation:

11 = 3 – 7x.

__Solution__

In this, case we can still isolate the variable x to the right side of the equation.

Subtract 3 from both sides of the equation.

=> 11 – 3 = 3 – 3 – 7x

8 = – 7x

Divide both sides of the equation by -7 to isolate for x.

=> 8/-7 = -7/7x

x = -1.14

*Practice Questions*

Solve for x in the following (1-10) two step equations:

- 7x + 9 = 23
- x/5 + 7 = -3
- x/5 – 8 = 7
- 5x – 6 = 3(x-1)
- 1/4x + 7 = -9
- 23 = (x/3) +6
- 2x/5 – 3/10 = 9/10
- 2x + 5 = 21
- – 3x – 8 =20
- -4x + 7 = 15
- The sum of three consecutive integers is 99. Find the biggest of these numbers.
- There are 272 students in a school and there are 7 classrooms in total. If one classroom has 8 students and rest of the classrooms have same number of students, how many students are there is each of the remaining 6 classrooms?
- The sum of three consecutive even integers is 96. Find the biggest of these numbers.

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