Can linear equations and linear inequalities be solved the same way? - Answers

Yes, but with the following two rules to remember. If you multiply or divide both sides by a negative number, then the inequality sign is reversed (> becomes <, or < becomes >). Adding and subtracting numbers have no effect on the direction of the inequality. Also, if you have a 'not equals' sign, then it is unaffected by the multiplication. The same is true if you take the reciprocal of both sides. Example: with the equation: 1/x = 2, take the reciprocal and x = 1/2. With the inequality 1/x < 2, this becomes x > 1/2. You could also solve it by multiplying both sides by x, then dividing both sides by 2, and get 2 < x, which is the same as x > 2. Another example: 3 - x > 7. Subtract 3 from both sides: -x > 4. Multiply both sides by -1: x < -4. You could also go about this as: add x to both sides: 3 > 7 + x, then subtract 7 from both sides: -4 > x, which means the same as x < -4