Linear equation in one variable

Linear equation in one variable

• 2.
  Linear equation inone variable: An equation of one variable and first order is called a linear equation in one variable such an equation has only one solution. A solution is also called the ‘root’ of the given equation. An equation that can be written in the form, ax + b = 0, Where a and b are real numbers and a ≠ o. Following are some examples: a) 2x + 3 = 0 x 1 2 b) 3 2 3 + = c) 5(3x+2) - 2 = - 2(1-7x)
• 3.
  Example-1 Solve the equationx – 4 = 5. Solution: Since x – 4 = 5 x = 5 + 4 x = 9 Example-2 Solve the equation 3x – 4 = 5. Solution: Since 3x – 4 = 5 3x = 5 + 4 3x = 9 9 x 3 = x = 3
• 4.
  Example-3 Solve the equation3-{2(1-x)-x} = 4 Solution: Since 3-{2(1-x)-x} = 4 3-{2-2x-x} = 4 3-(2-3x) = 4 3-2+3x = 4 1+3x = 4 3x = 4-1 3x = 3 3 x 3 = x = 1
• 5.
  Example-4 Solve the equation x5 x 3 5 7 4 14 + − + = Solution: x 5 x 3 5 since 7 4 14 4(x 5) 7(x 3) 5 28 14 4x 20 7x 21 5 2 + − + = + + − = + + − = 11x 1 5 2 11x 1 5x 2 11x 1 10 11x 10 1 11x 11 11 x 11 x 1 − = − = − = = + = = =
• 6.
  Example-5 Solve the equation x(x 3) 1 4 6 − − = Solution: x (x 3) 1 4 6 multiplying throghout by the LCM (2 x 2 x 3) of the denominators (which is 12) x 3x 12 12 12(1) 64 3x 2(x 3) 12 3x 2x 6 12 x 6 12 x 12 6 x 6 − − = −  − =        − − = − + = + = = − =