SOLVING INEQUALITIES LESSON 6(2)

Solving Inequalities Just like with equations, the solution to an inequality is a value that makes the inequality true. You can solve inequalities in the same way you can solve equations, by following these rules.

Steps to Solving Inequalities You may add any positive or negative number to both sides of an inequality. You may multiply or divide both sides of an inequality by any positive number. Watchout! If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign!

Symbols of Inequalities MEANING > “IS GREATER THAN” < “IS LESS THAN”  “IS GREATER THAN OR EQUAL TO”  “IS LESS THAN OR EQUAL TO”

EXAMPLE 1 2x - 3 < 5x + 15 2x - 3 + 3 < 5x + 15 + 3 Solve: 2x - 3 < 5x + 15 EXAMPLE 1 2x - 3 < 5x + 15 2x - 3 + 3 < 5x + 15 + 3 2x < 5x + 18 2x - 5x < 5x - 5x + 18 -3x < 18 Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign. -3x -3 18 -3 < x > -3

YOU TRY Solve: 3x +4 < 6x + 12 Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign.

SOLUTION 2x +4 < 6x + 12 2x + 4 - 4 < 6x + 12 - 4 2x < 6x + 8 Solve: 3x +4 < 6x + 12 SOLUTION 2x +4 < 6x + 12 2x + 4 - 4 < 6x + 12 - 4 2x < 6x + 8 2x - 6x < 6x - 6x + 8 -4x < 8 Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign. - 4x - 4 8 - 4 < x > -2

EXAMPLE 2 2(x - 3) < 5(x + 3) 2x - 6 < 5x + 15 Solve: 2(x - 3) < 5(x + 2) EXAMPLE 2 2(x - 3) < 5(x + 3) 2x - 6 < 5x + 15 2x - 6 + 6 < 5x + 15 + 6 2x < 5x + 21 2x - 5x < 5x - 5x + 21 -3x < 18 Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign. -3x -3 21 -3 < x > -7

YOU TRY Solve: -2(x - 4)  4(x + 4) Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign.

SOLUTION -2(x - 4)  4(x + 4) -2x +8  4x + 16 Solve: -2(x - 4)  4(x + 4) SOLUTION -2(x - 4)  4(x + 4) -2x +8  4x + 16 -2x +8 - 8  4x + 16 - 8 -2x  4x + 8 -2x - 4x  4x - 4x + 8 -6x  8 Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign. -6x -6 8 -6  1 3 x  -1

[ ] [ ] EXAMPLE 3 1 2 2 3 2 3 1 2 (2 + 5x) < (15 - 3x) 2 3 1 2 6 Solve: (2 + 5x) < (15 - 3x) EXAMPLE 3 1 2 2 3 2 3 1 2 (2 + 5x) < (15 - 3x) Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign. [ 2 3 ] [ 1 2 ] 6 (2 + 5x) < 6 (15 - 3x) 3(2 + 5x ) < 4(15 - 3x) 6 + 15x < 60 - 12x 6 - 6 + 15x < 60 - 6 - 12x 15x < 54 - 12x 15x + 12x < 54 - 12x + 12x 27x < 54 27x 27 54 27 x < 2 <

YOU TRY 1 2 2 3 Solve: (2 - 3x)  (5 +2x) Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign.

[ ] [ ] SOLUTION 1 2 2 3 2 3 1 2 (2 - 3x)  (5 + 2x) 2 3 1 2 6  6 Solve: (2 - 3x)  (5 +2x) SOLUTION 1 2 2 3 2 3 1 2 (2 - 3x)  (5 + 2x) Things to Remember: Did you isolate the variable? Do you need to Expand? Do you need to get rid of a fraction? Do you have to divide by the number in front of the variable? Do you have to collect like terms first? 6. Did you multiply or divide by a negative number - therefore reverse the sign. [ 2 3 ] [ 1 2 ] 6 (2 - 3x)  6 (5 + 2x) 3(2 - 3x )  4(5 + 2x) 6 - 9x  20 + 8x 6 - 6 + 9x  20 - 6 + 8x 9x  14 + 8x 9x - 8x  14 + 8x - 8x x  14 x  14

CLASS WORK Check solutions to Lesson 6 Copy down examples from this lesson Do Lesson 6(2) worksheet