6 1 Solving inequalities by addition and subtraction

6 -1: Solving inequalities by addition and subtraction n n Addition property of inequalities If any number is added to each side of a true inequality, the resulting inequality is also true. For example: 3<8 3+2 < 8+2 5 < 10 Example 1: Solve s -12 > 65 +12 s > 77 Which means all numbers greater then 77 will work. n

Example 2 n n n To graph the solution on a number line. Find the answer. Draw a number line Pay attention to the starting point (open circle for < or > & closed circle for < or > ) Which way do I shade? 12 > y – 9 +9 +9 21 > y Switch it to be y < 21. Set-builder notation: {y | y < 21} n 17 21 24

Subtraction n n Subtraction property of inequalities If any number is subtracted from each side of a true inequality, the resulting inequality is also true. For example: 3<8 3 -2 < 8 -2 1<6 Example 3: q + 23 14 -23 q > -9 Solution set: {q | q -9} Graph n -12 -9 -6

Variable on both sides n n Get the variable on one side, numbers without variables on the other side. Simplify. 12 n – 4 ≤ 13 n -12 n -4 ≤ n or n > -4 Solution set: { n | n -4} n -8 -4 -1

Write and solve an inequality n n n Seven times a number is greater than six times that number minus two. 7 x 7 x > 6 x – 2 Solve. 7 x > 6 x – 2 -6 x x > -2 Solution set: {x | x > -2} n -6 -2 1

Your Turn Homework #39 n p. 297 12 -34 even, 37, 39, 41, 51 -53 n