Test for Linear Equations:

Linear equations are an important topic in mathematics, especially in algebra. They involve equations in which the highest power of the variable is 1. Solving linear equations helps in finding the value of an unknown variable. Here is a test for linear equations designed for Class 8 students:

Test for Linear Equations:

1. Solve the following equations:
a) 3x + 4 = 16
b) 2(2x - 5) = 18
c) 5(x + 3) - 2x = 12

2. Write an equation for the statement: "Three more than twice a number is equal to 11."

3. Solve the equation: 2(x - 3) + 5 = 13

4. Solve the following equation for x: 4(x - 2) - 3(2x + 1) = 5

5. The sum of two numbers is 15. If one of the numbers is x, write an equation to represent the situation.

6. Solve the equation: 3x - 7 = 2(x + 4)

7. The length of a rectangle is 5 more than twice its width. If the width is x, write an equation for the length.

8. Solve the equation: 2(3x + 1) = 4x - 5

9. The perimeter of a rectangle is 36 cm. If the length is 2 cm more than twice the width, write an equation for the perimeter.

10. Solve the equation: 4(2x - 3) = 3(4 - 2x)

Solutions:
1. a) x = 4
b) x = 14
c) x = 7

2. Let the number be x. The equation is: 2x + 3 = 11

3. x = 10

4. x = 7

5. x + (15 - x) = 15

6. x = -15

7. Length = 2x + 5

8. x = 3

9. Perimeter = 2(2x + 2) + 2x = 36

10. x = -3

By solving these equations, students will practice their understanding of linear equations and their ability to find the value of unknown variables. It is important to emphasize the steps involved in solving each equation, such as combining like terms, isolating the variable, and simplifying the equation.