Warm-up: Solve for x. 6x + 12 = -15 + 3x 2x + 3(x – 5) = 25

1. x + 3 < 6 ; 5 2. 2x – 3 > -3 ; 1 3. 4x – 1  3x + 2 ; 3 Determine whether the given number is a solution of the inequality. 1. x + 3 < 6 ; 5 2. 2x – 3 > -3 ; 1 3. 4x – 1  3x + 2 ; 3 False, not a solution 8 < 6 True, it is a solution 2 – 3 > -3 -1 > -3 True, it is a solution 12 – 1  9 + 2 11  11

Graphing One Variable Inequalities

Solving Multi-step Equations & Inequalities Distribute. 2. Combine like terms. 3. Move variable to the left side if needed (add or subtract) 4. Get rid of constant (add or subtract) 5. Get rid of coefficient or denominator (divide or multiply) **Be careful – Dividing or Multiplying by a Negative will switch your inequality sign**

Inequality Signs When graphing the number use a … Closed Circle <  > OPEN Circle <  >

Graph Using a Number Line -3 2 Opened Circle Closed Circle Shade to the left Shade to the right

Solve, then graph. 3. x + 4 > 7 -4 -4 x > 3

Try These: Solve then graph.

Graphing Linear Inequalities

Checking Solutions 3x + 2y ≥ 2 An ordered pair (x,y) is a solution if it makes the inequality true. Are the following solutions to: 3x + 2y ≥ 2 1. (0,0) 2. (2,-1) 3. (0,1) 3(0) + 2(1) ≥ 2 2 ≥ 2 Is a solution 3(0) + 2(0) ≥ 2 0 ≥ 2 Not a solution 3(2) + 2(-1) ≥ 2 4 ≥ 2 Is a solution

Write in Slope-Intercept Form 2y < 8x + 10 5. 2x – y > -3 Solid or Dashed?? Solid or Dashed??

To sketch the graph of a linear inequality: Sketch the line given by the equation (solid if ≥ or ≤, dashed if < or >). This line separates the coordinate plane into 2 halves. In one half-plane – all of the points are solutions of the inequality. In the other half-plane - no point is a solution 2. You can decide which half to shade by testing ONE point. 3. Shade the half that has the solutions to the inequality.

Graph the inequality 6. y ≥ -3/2x + 1 Graph the line Before you connect the dots check to see if the line should be solid or dashed solid if ≥ or ≤ dashed if < or >

6. y ≥ -3/2x + 1 Step 1: Graph the boundary (the line is solid ≥) Step 2: test a point NOT on the line (0,0) is always the easiest if it’s Not on the line!! (0) ≥ -3/2(0) + 1 0 ≥ 1 Not a solution So shade the other side of the line!!

7. Graph: y < 6

8. 4x – 2y < 6

9. 2x – 6y > 18