How to Solve Algebraic Equations in Grade 8 with Step by Step Practice Worksheets
Algebraic equations form a major part of the Class 8 mathematics curriculum and are considered essential for mastering algebra in higher grades. Understanding how to solve 8th grade algebraic equations worksheets builds a solid foundation for handling equations, which are crucial for school exams, olympiads, and even daily problem-solving scenarios. Regular practice with algebraic equations not only improves confidence but also enhances logical thinking and analytical skills.
What Are Algebraic Equations?
An algebraic equation is a mathematical statement that shows two expressions are equal, often involving an unknown value called a variable (commonly written as x, y, or z). Solving an equation means finding the value of the variable that makes the equation true. For example, in the equation 2x + 5 = 11, we find the value of x that satisfies this equality.
Key concepts related to algebraic equations include:
- Variable: A symbol representing an unknown number (e.g., x in 3x + 2 = 8).
- Constant: A fixed number (e.g., 2 in 3x + 2).
- Equation: A statement of equality (e.g., 2y – 5 = 11).
- Balancing: Keeping both sides of the equation equal by performing the same operation on both sides.
Types of Algebraic Equations in Class 8
In 8th grade, you will encounter several types of algebraic equations. Understanding each type will help you solve questions efficiently:
| Type | Example | Description |
|---|---|---|
| One-step equation | x + 7 = 12 | Solved in one step (addition, subtraction, multiplication, or division). |
| Two-step equation | 3x - 5 = 10 | Requires two inverse operations to solve. |
| Multi-step equation | 2x + 7 = 3x - 5 | Variables on both sides; needs moving terms and simplifying. |
| Equations with brackets | 2(x + 3) = 12 | Involves the distributive property to expand. |
| Word problems | A number plus 5 is 17. Find the number. | Requires setting up an equation from context. |
How to Solve Algebraic Equations (Step-by-Step)
To solve any algebraic equation:
- Isolate the variable on one side using addition/subtraction.
- Use inverse operations to remove coefficients or constants.
- Simplify until only the variable is left.
- Check your solution by substituting it back into the original equation.
Let's solve 2x + 5 = 13:
- Subtract 5 from both sides: 2x = 8
- Divide by 2: x = 4
- Check: 2(4) + 5 = 8 + 5 = 13 (Correct!)
Important Algebraic Formulae for Grade 8
Knowing these formulas and properties can help solve equations efficiently:
- Distributive Property: a(b + c) = ab + ac
- Algebraic Identities (for expressions):
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
a2 - b2 = (a + b)(a - b)
Worked Examples
Example 1: One-step Equation
Solve x – 9 = 4
- Add 9 to both sides: x = 4 + 9 = 13
- Check: 13 – 9 = 4
Example 2: Word Problem
If 3 times a number is 18, what is the number?
- Let the number be x. 3x = 18
- Divide by 3: x = 6
- Check: 3 × 6 = 18
Example 3: Equation with Variables on Both Sides
Solve 2x + 3 = x + 8
- Subtract x from both sides: 2x – x + 3 = 8 ⇒ x + 3 = 8
- Subtract 3: x = 5
- Check: 2(5) + 3 = 10 + 3 = 13; 5 + 8 = 13
Practice Problems
- Solve: 4x – 6 = 10
- Solve: 7y + 2 = 23
- Solve: 5a – 3 = 2a + 12
- What is the number that when multiplied by 8 gives 40?
- Solve: 2(x + 5) = 16
Common Mistakes to Avoid
- Forgetting to perform the same operation on both sides of the equation.
- Mistaking variables for constants or vice versa.
- Making sign errors when moving terms across the equation.
- Not simplifying the final answer fully (e.g., leaving as 2x = 8 instead of x = 4).
- Not checking the solution in the original equation.
Real-World Applications
Algebraic equations are used in daily life for budgeting, comparing prices, planning journeys, and more. For example, if a bus ticket costs ₹25 and you spend a total of ₹200, you can use an equation (25x = 200) to find out how many trips you made. At Vedantu, we simplify complex topics like linear equations and algebraic expressions to help students master both exam-style questions and real-life scenarios.
Solving 8th grade algebraic equations worksheets and practicing different types of equation problems helps students build confidence, accuracy, and speed—skills necessary for success in school and competitive exams. Regular practice with well-designed worksheets and concept explanations, like those at Vedantu, nurtures a deep love for mathematics and prepares learners for future academic challenges.
FAQs on 8th Grade Algebraic Equation Worksheets for Solving Linear Equations
1. What are algebraic equations in 8th grade?
An algebraic equation in 8th grade is a mathematical statement that shows two expressions are equal and contains one or more variables. It usually involves solving for an unknown value such as x or y.
- An equation has an equal sign (=).
- It includes numbers, variables, and operations (+, −, ×, ÷).
- Example: 2x + 5 = 15.
- Solving means finding the value of x that makes the equation true.
2. How do you solve a one-step algebraic equation?
To solve a one-step algebraic equation, use the inverse operation to isolate the variable. This means undoing the operation attached to the variable.
- Example: x + 7 = 12
- Subtract 7 from both sides: x = 12 − 7
- x = 5
3. How do you solve a two-step algebraic equation?
To solve a two-step equation, undo addition or subtraction first, then undo multiplication or division. The goal is to isolate the variable step by step.
- Example: 3x + 4 = 19
- Step 1: Subtract 4 → 3x = 15
- Step 2: Divide by 3 → x = 5
- x = 5
4. What is the distributive property in algebraic equations?
The distributive property states that a(b + c) = ab + ac. It is used to remove parentheses in algebraic equations.
- Example: 2(x + 3) = 14
- Distribute 2: 2x + 6 = 14
- Subtract 6: 2x = 8
- Divide by 2: x = 4
5. How do you check your answer in an algebraic equation?
To check an algebraic equation, substitute the solution back into the original equation and verify both sides are equal. This confirms the solution is correct.
- Example: If x = 5 in 2x + 5 = 15
- Substitute: 2(5) + 5 = 10 + 5 = 15
- Since both sides equal 15, x = 5 is correct.
6. What is the difference between an expression and an equation?
An algebraic expression does not contain an equal sign, while an algebraic equation includes an equal sign and can be solved. Expressions are simplified, but equations are solved.
- Expression: 3x + 4
- Equation: 3x + 4 = 10
- Equations have solutions; expressions do not.
7. How do you solve equations with variables on both sides?
To solve equations with variables on both sides, move all variable terms to one side and constants to the other side. Then simplify and solve.
- Example: 5x − 3 = 2x + 9
- Subtract 2x: 3x − 3 = 9
- Add 3: 3x = 12
- Divide by 3: x = 4
8. What are like terms in algebra?
Like terms are terms that have the same variable raised to the same power. Only the coefficients can be different.
- Example of like terms: 4x and 9x
- Example of unlike terms: 3x and 3x²
- Combine like terms: 4x + 9x = 13x
9. What is a linear equation in one variable?
A linear equation in one variable is an equation where the highest power of the variable is 1. It forms a straight-line relationship when graphed.
- Standard form: ax + b = 0
- Example: 2x + 6 = 0
- Solving: 2x = −6 → x = −3
10. What are common mistakes when solving algebraic equations?
Common mistakes in solving algebraic equations include not applying inverse operations correctly and forgetting to perform the same operation on both sides. Avoiding these errors improves accuracy.
- Forgetting to distribute properly.
- Not combining like terms.
- Changing signs incorrectly.
- Failing to check the final answer.
