Graphing Inequalities and Equation Solutions October 3, 2016

Outline Graphing directions Graphing Less than and Greater than Inequalities Graphing Less than or Equal to and Greater than or Equal to Inequalities Examples Solution Types for Equations

Graphing Instructions Draw a number line that includes numbers before and after solution. If the symbol is < or >, then put an open circle over the number in the solution. If the symbol is ≤𝑜𝑟≥ then put a closed circle over the number in the solution. Draw an arrow in the direction of symbol (i.e. if the symbol is < then draw an arrow pointing ←)

Graphing Less than and Greater than Inequalities x < 9 -1 1 2 3 9 Less Than (<) x < -5 -6 -5 -2 -1

Graphing Less than and Greater than Inequalities x > -6 -6 -5 -1 1 2 3 Greater Than (>) x > 7 1 2 7 8

Graphing Less than or Equal to Inequalities x ≤ 10 -1 1 2 3 10 Less Than or Equal to (≤) x ≤ -6 -6 -5 -2 -1

Graphing Greater than or Equal to Inequalities x ≥ -5 -6 -5 -1 1 2 3 Greater Than or Equal to (≥) x ≥ 8 1 2 7 8

Example Step 1: x +20 < 39 Step 2: x +20 - 20 < 39 - 20 x < 19 (All numbers less than 19) 1 19

Example Step 1: x -12 > 25 Step 2: x -12 +12 > 25 +12 x > 37 (All numbers greater than 37) 37 38

Example Step 1: d - 8 ≥ 24 Step 2: d -8 + 8 ≥ 24 + 8 d ≥ 32 (All numbers greater than or equal to 32) 31 1 32

Example Step 2: ( 17𝑦 17 ) ≤ ( 68 17 ) Step 3: ( 17𝑦 17 ) ≤ ( 68 17 ) Step 1: 17y ≤ 68 Step 2: ( 17𝑦 17 ) ≤ ( 68 17 ) Step 3: ( 17𝑦 17 ) ≤ ( 68 17 ) y(1) ≤ (4) y ≤ 4 (All numbers less than or equal to 4) 3 4

Equation Solutions Infinite Solutions Occurs when both sides of an equation equal zero Example 2y+6=2y+6 2y+6-6=2y+6-6 2y+0=2y+0 2y=2y 2y-2y=2y-2y 0=0 (True)

Equation Solutions No Solutions Occurs when one side of an equation equals zero and the other side is a non-zero integer Example 4d+8=4d+6 4d+8-8=4d+6-8 4d+0=4d-2 4d=4d-2 4d-4d=4d-4d-2 0=-2 (False)

Solving for Variable Problem 1: Solve the following equation for L A=LW 𝐴 𝑊 = 𝐿𝑊 𝑊 𝐴 𝑊 = L L= 𝐴 𝑊 Problem 2: Solve the following equation for A B=A+C B-C=A+C-C B-C=A A=B-C

Example 4g-12=4(g-3) 4g-12=4g-12 4g-12+12=4g-12+12 4g+0=4g+0 4g=4g 0=0 Infinite Solutions

Example 7h-13=7h+13 7h-13+13=7h+13+13 7h+0=7h+26 7h=7h+26 0=26 No Solutions