# Class 08 - Chapter 02 - Linear Equations in One Variable (75)

Posted in Class VIII

Note:

An algebraic equation is an equality involving variable. It has an equality sign. The expression on the left of the equality sign is the Left Hand Sign (LHS). The expression on the right of the equality sign is the Right Hand Sign (RHS).

In an equation the values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variable. These values are the solutions of the equation.

How to find the solution?

We assume that the two sides of the equation are balanced. We perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed. A few such steps give the solution.

Solve the following equations:

Q.1. $$x - 3 = 10$$

Q.2. $$p + 10 = 11$$

Q.3. $$7 + p = 12$$

Q.4. $$12 - y = 3y - 5$$

Q.5. $$\frac{5}{7} + y = \frac{12}{7}$$

Q.6. $$\frac{x}{10} = 2$$

Q.7. $$\frac{10}{x} = 2$$

Q.8. $$\frac{x}{5} - 2 = 1$$

Q.9. $$\frac{3x}{2} + 2 = -x$$

Q.10. $$\frac{x}{3} + 1 = \frac{1}{3}$$

Q.11. $$12y - 10 = 12 - 10y$$

Q.12. $$10x \div 3 = 2$$

Q.13. $$7x + 3 - 2x = x + 25$$

Q.14. $$4x - 2 = 3x - 7$$

Q.15. $$2x = x + 20$$

Q.16. $$7x + 12 = 24 + 3x$$

Q.17. $$15 - 2x = 7 - 3x$$

Q.18. $$6x - 1 = 3 ( x - 12 ) + 2$$

Q.19. $$y = \frac{2}{3} ( y + 20 )$$

Q.20. $$\frac{2x}{3} + 2 = \frac{3x}{15} - 3$$

Q.21. $$2p = 3p - \frac{1}{5}$$

Q.22. $$\frac{p}{2} - \frac{2p}{3} + \frac{p}{6} = 10$$

Q.23. $$\frac{2y}{3} + \frac{2}{6} = \frac{y}{3} + \frac{4}{3}$$

Q.24. $$y + \frac{y}{4} = 20$$

Q.25. $$y + \frac{2y - 3}{2} = 1 - \frac{ y + 2 }{2}$$

Q.26. $$2 ( x - 12 ) = 4 ( 2x - 12 )$$

Q.27. $$0.50 ( 4y - 7 ) = 0.125 ( 8y - 9 )$$

Q.28. $$2 (5y - 3) - 4 (y - 7) = 7 (2 - y)$$

Q.29. $$10 (y + 2) - (12 + y) + 5 (12 - y) = 0$$

Q.30. $$\frac{1}{3} ( x - 3) = \frac{2}{5} (2x - 7)$$

Q.31. $$\frac{2x - 3}{x + 4} = 1$$

Q.32. $$\frac{6x}{5x - 3} = 1$$

Q.33. $$\frac{x - 2(x + 3) - 3}{7x} = 0$$

Q.34. $$\frac{x + 12}{7x - 4(2x - 45) - 7 (x + 34) - 500} = 0$$

Q.35. $$\frac{2y + 7}{4} = \frac{3- 2y}{3}$$

Q.36. $$\frac{y - 7}{3} + y = \frac{5 - 3y}{2} - 1$$

Q.37. $$\frac{2y}{y + 19} = \frac{3}{5}$$

Q.38. $$1 + \frac{9y}{y + 8} = \frac{3}{2}$$

Q.39. $$x + \frac{2}{3} - \frac{x + 1}{6} = \frac{6 - 2x}{2} - 1$$

Q.40. $$\frac{7 + 2 ( 3x - 4) + 3 (3 - 45x)}{9 - 2 (11 - x) + 2 (12 + x)} = 0$$