How to Solve Two Step Linear Equations?

Two Step Equations comes under the parent topic Algebra which helps in representing the problem in the form of mathematical expressions. Algebra is the study of mathematical symbols and rules for manipulating the symbols. Algebraic expressions include constants, variables like x, y, z, a, b, etc, and mathematical operators like addition, subtraction, multiplication division between variables.

Two Step Equations

Two Step Equations are equations that can be solved by only two steps. These equations are easy to solve but a little complicated when compared to one-step equations. In solving the two-step equations, Arithmetic operations are performed on both sides of equal to symbol. The two-step equations are algebraic problems that can be solved in two steps. Here variable is isolated on one side of “=” to find its value. The general form of two-step equations is ax + b = c where a, b, c are real numbers.

Examples: 2x + 3 = 0, 7a – 5 = 2, (2/3)x + 1 = 4

Steps to solve Two Step Equations

These Two-Step Equations can be solved easily. It needed just one more step extra as compared to solving one-step equations. The variable is isolated on one side of “=” to determine its value. The steps needed are mentioned below,

  1. Add or Subtract to isolate the variable.
  2. Multiply or Divide to find the value of a variable.

Sample Problems

Question 1: Solve the equation 3x + 3 = 12

Solution:

Given two step equation 3x + 3 = 12

Step 1: Subtract 3 from both sides.

3x + 3 – 3 = 12 – 3

3x = 9

Step 2: Divide the equation with 3 on both sides

(3x/3) = (9/3)

x = 3

This can be verified by substituting x = 3 in the given equation,

3(3) + 3 = 12

9 + 3 = 12

12 = 12

Hence it was proved that on solving the given equation, we got x = 3.

Question 2: Solve the equation x – 5 = 2

Solution:

Given two step equation x – 5 = 2

Step 1: Add 5 to both sides.

x – 5 + 5 = 2 + 5

x = 7

As the coefficient of variable is 1, No need to perform the step 2. The above result can be verified by substituting x = 7 in the given equation.

x – 5 = 2

7 – 5 = 2

2 = 2

Hence it was proved that on solving the given equation, we got x = 7.

Question 3: Solve the equation (x/2) – 5 = 5

Solution:

Given two step equation (x/2) – 5 = 5

Step 1: Add 5 to both sides.

(x/2) – 5 + 5 = 5 + 5

(x/2) = 10

Step 2: Multiply the equation with 2 on both sides,

(2x/2) = 10 x 2

x = 20

This can be verified by substituting x = 20 in the given equation,

(x/2) – 5 = 5

(20/2) – 5 = 5

10 – 5 = 5

5 = 5

Hence it was proved that on solving the given equation, we got x = 20.

Question 4: Solve the equation (2x/3) + 6 = 0

Solution:

Given two step equation (2x/3) + 6 = 0

Step 1: Subtract 6 from both sides.

(2x/3) + 6 – 6 = 0 – 6

(2x/3) = -6

Step 2: Multiply the equation with 3/2 on both sides,

(2x/3) x (3/2) = -6 x (3/2)

(6x/6) = (-18/2)

x = -9

This can be verified by substituting x = -9 in the given equation,

(2x/3) + 6 = 0

(2(-9)/3) + 6 = 0

(-18/3) + 6 = 0

(-18 + 18)/3 = 0

(0/3) = 0

0 = 0

Hence it was proved that on solving the given equation, we got x = -9.

Question 5: Solve the equation 4a – 2.6 = 1.4

Solution:

Given two step equation 4a – 2.6 = 1.4

Step 1: Add 2.6 to both sides.

4a – 2.6 + 2.6 = 1.4 + 2.6

4a = 4

Step 2: Divide the equation with 4 on both sides,

(4a/4) = (4/4)

a = 1

This can be verified by substituting a = 1 in the given equation,

4a – 2.6 = 1.4

4(1) = 1.4 + 2.6

4 = 4

Hence it was proved that on solving the given equation, we got a = 1.

Question 6: Solve the equation 2z + 1.5 = 2.3

Solution:

Given two step equation 2z + 1.5 = 2.3

Step 1: Subtract 1.5 from both sides.

2z + 1.5 – 1.5 = 2.3 – 1.5

2z = 0.8

Step 2: Divide the equation with 2 on both sides

(2z/2) = (0.8/2)

z = 0.4

This can be verified by substituting z = 0.4 in the given equation,

2z + 1.5 = 2.3

2(0.4) = 2.3 – 1.5

0.8 = 0.8

Hence it was proved that on solving the given equation, we got z = 0.8.

Question 7: Solve the equation 1.2a – 1.2 = 1.2

Solution:

Given two step equation 1.2a – 1.2 = 1.2

Step 1: Add 1.2 to both sides.

1.2a – 1.2 + 1.2 = 1.2 + 1.2

1.2a = 2.4

Step 2: Divide the equation with 1.2 on both sides.

(1.2a/1.2) = (2.4/1.2)

a = 2

This can be verified by substituting a = 2 in the given equation,

1.2a – 1.2 = 1.2

1.2(2) – 1.2 = 1.2

2.4 – 1.2 = 1.2

1.2 = 1.2

Hence it was proved that on solving the given equation, we got a = 2.

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