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# Download (a) Describe in your own words how to solve a linear equation using

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(a) Describe in your own words how to solve a linear equation using the equality properties. Demonstrate the process with an example. bNext, replace the equal sign in your example with an inequality by using the less than or greater than sign. Then solve the inequality. (c) What similarities do you see in solving equations and inequalities? What differences to you see? (a) To solve a linear equation, we perform the same mathematical operation on both sides of the equation. We do this so that we ultimately get only the variable to be solved on the left side and everything else on the right side. Consider the problem: Solve (5x - 11)/6 = 4 Multiply both sides by 6 to get 5x - 11 = 24 Add 11 to both sides to get 5x = 35 Divide both sides by 5 to get x = 7 The solution is x = 7 (b) Consider the problem: Solve (5x - 11)/6 > 4 Multiply both sides by 6 to get 5x - 11 > 24 Add 11 to both sides to get 5x > 35 Divide both sides by 5 to get x > 7 The solution is {x| x > 7} (c) It is easy to observe from the solutions of (a) and (b) above that the procedure of solving an equation and an inequality is the same. But the difference is that while a linear equation has one and only one solution, a linear inequality has a range of solutions. In our example, the equation (5x - 11)/6 = 4 has just one solution, x = 7, while the inequality (5x - 11)/6 > 4 has many solutions (any real number greater than 7 is a solution).