6.1 Solving Inequalities with adding and subtracting

1. 6.1 Solving Inequalities with adding and subtracting • graph inequalities on a number line. • solve inequalities using addition and subtraction. SOL: A.1, A.3 Designed by Skip Tyler, Varina High School Edited by Eddie Judd, Crestwood Middle School

2. o 1) Graph the solution set ofx < 3. When you have < or >, use an open dot!

3. • 2) Graph the solution set ofy ≥ -5/4. When you have ≤ or ≥, use a closed dot! Converting -5/4 to a decimal = -1.25

4. o 3) Graph the solution set ofp ≠ 2. When you have ≠, use an open dot and shade both ways!

5. Answer Now 4) Which inequality would have a closed dot on the number line? • > • < • ≥ • ≠

6. Answer Now 5) Which inequality does NOT use an open dot on the number line? • ≤ • < • > • ≠

7. o 29 30 31 6) Solve x + (-14) < 16 • Solve this problem like an equation • Draw “the river” • Eliminate double signs • Add 14 to both sides • Simplify Set Notation • Check your limit • Graph the solution x- 14< 16 + 14 + 14 {x|x < 30} 30 + (-14) = 16 16 = 16

8. ● -15 -14 -13 7) Solve y + 21 ≥ 7 • Draw the “river” • Subtract 21 from both sides • Simplify in Set Notation • Check your limit • Graph the solution - 21 -21 {y|y≥ -14} (-14) + 21 = 7 7 = 7

9. o 16 17 18 8) Solve 8y + 3 > 9y - 14 - 8y - 8y 3 > y - 14 + 14 + 14 17 > y {y|y < 17} 8(17) + 3 = 9(17) - 14 • Draw “the river” • Subtract 8y from both sides • Simplify • Add 14 to both sides • Simplify • Rewrite inequality in Set Notation • Check your limit • Graph the solution

10. o 6 7 8 o 6 7 8 ● 6 7 8 6 7 8 Answer Now 9) What is the graph of 7 ≤ m? ●

11. ● 30 31 32 - 2r - 2r r – 17 ≥ 14 + 17 + 17 {r|r ≥ 31} 3(31) - 17 = 2(31) + 14 • Draw “the river” • Subtract 2r from both sides • Simplify • Add 17 to both sides • Simplify in Set Notation • Check your limit • Graph the solution 10) Solve 3r - 17 ≥ 2r + 14

12. Answer Now 11) Solve -2x + 6 ≥ 3x - 4 • {x|x ≥ -2} • {x|x ≤ -2} • {x|x ≥ 2} • {x|x ≤ 2}

13. Answer Now 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? • 96 • 97 • 98 • 100