Equations with a Variable on Both Sides - Examples and Questions with Answers

algebra Jun 02, 2021
Variables on both sides

What are Equations with a Variable on Both Sides?

Some algebra questions have the unknown variable on both sides of an equation. To solve those types of questions either we can add or subtract on both sides without changing the equation and then apply the inverse operation to get the value of the unknown variable.

Examples:

  • 3y + 10 = 2y + 15
  • 2x + 25 = 3x + 10

Types of Questions

It’s time to practice some algebraic questions on variables on both sides. First, we will solve direct equation problems and then we will deal with word-based problems.

Equations with a Variable on Both Sides - Direct Equation Questions

These type of questions involve solving the equations directly. 

Questions:

  1. Solve for y: 5y - 3 = 3y + 5
  2. Solve for p: 30 - 3p = 13p - 50
  3. Solve for m: 5m - 45 = 3 - 3m
  4. Solve for d: 2d + 13 = 5 + 6d
  5. Solve for p: 5p + 35 = 70 - 2p

Answers:

  1. 4
  2. 5
  3. 6
  4. 2
  5. 5

📄 Download Direct Equations Worksheet with Answers

 

Equations with a Variable on Both Sides - Bracket Expansion Questions

In this type of algebra questions first, we need to expand brackets after that it will be the same as solving the direct equation questions.

Questions:

  1. Solve for x: 4(x + 6) = 2(5x + 3)
  2. Solve for x: 6(2x + 3) = 3(5x - 2)
  3. Solve for x: 9(2x - 10) = 4(2x - 20)
  4. Solve for m: 4(m - 2) = 3(2 + m)
  5. Solve for y: 5y - 4 = 2(8 + 2y)

Answers:

  1. 3
  2. 8
  3. 1
  4. 14
  5. 20

📄 Download Bracket Expansion Worksheet with Answers

 

Equations with a Variable on Both Sides - Word Problems

In this type of questions first, we have to convert given questions into mathematical equations. After that, we can solve it by the general method as shown above in equation-based questions.

Questions:

  1. Four times a number, decreased by 4, is the same as thrice the number increased by 6. Find the number.
  2. Two times a number, decreased by 4, is the same as 1.5 times the number. Find the number.
  3. What is the value of p, if opposite sides of the rectangle are 2p + 2 and p + 8?
  4. Four times a number, increased by 6, is the same as six times a number, decreased by 6. Find the number. 
  5. What is the value of k, if the adjacent sides of the square are 5k + 5 and 3k + 35?

Answers:

  1. 4
  2. 8
  3. 10
  4. 6
  5. 15

📄 Download Variable on Both Sides Word Problem Worksheet with Answers

 

How to Solve Equations with a Variable on Both Sides?

Type 1: Direct Equation Question

Question: Solve for p: 5p + 35 = 70 - 2p

Solution:


 

Type 2: Bracket Expansion Question

Question: Solve for y: 5y - 4 = 2(8 + 2y)

Solution:


 

Type 3: Word Problem

Question: What is the value of k, if the adjacent sides of the square are 5k + 5 and 3k + 35?

Solution:

 

To learn more about 11+ Advanced Algebra topics, word problems and how to solve them, view our video lessons on Advanced Algebra Word Problems for 11+ Exams.

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