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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 that 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 will take you **step by step in solving two-step equations** to make you familiar and proficient with the process.

Generally, when solving an equation, we apply the Law of Equations, which states that whatever 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** has been solved if a variable, usually represented by an alphabetical letter, is isolated on either the equation’s left or right side. The number is located on the opposite side.

## How to Solve Two-step Equations?

Solving a two-step equation involves working backward concerning the order of operations (PEMDAS). In this case, multiplication and division are 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 of 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