1. 1.5 L INEAR E QUATIONS AND I NEQUALITIES

2. Q UIZ Tell true or false of the following statement: If c bc.

3. L INEAR E QUATION A linear equation in one variable is an equation that can be written in the form: ax+b=0, a≠0

4. L INEAR E QUATION Addition and Multiplication Properties of Equality 1, if a=b, then a+c=b+c for any c ∈ R 2, If c≠0, a=b, then ac=bc, a/c=b/c.

5. S OLVE A LINEAR EQUATION ANALYTICALLY Find the zero of the function f. 1, f(x)=-3x-12 2, f(x)=-4(2x-3)+8(2x+1)

6. S OLVE A LINEAR EQUATION BY GRAPH To solve the equation f(x)=g(x) graphically, graph The x-coordinate of any point of intersection of the two graphs is a solution of the equation. y 1 =f(x) and y 2 =g(x)

7. S OLVE A LINEAR EQUATION BY GRAPH X-Intercept Method of Graphical Solution To solve the equation f(x)=g(x) graphically, graph Any x-intercept of the graph of y = F(x) is a solution of the equation. Recall: x-intercept is the zero of the linear function. y =f(x) -g(x)=F(x)

8. I DENTITIES AND C ONTRADICTIONS Identity : an equation that is true for all values in the domain of its variables. ex: 5(x+1)=5x+5 Contradiction : an equation that has no solution. ex: x+1=x+3

9. I NEQUALITIES IN O NE V ARIABLE Notation: a<ba>ba≤ba≥b a is less than b a is greater than b a is less or equal to b a is greater or equal to b

10. A DDITION AND M ULTIPLICATION P ROPERTIES OF I NEQUALITY For real numbers a, b and c 1, if a < b, then a + c < b + c. 2, If a 0, then ac < bc 3, if a bc Slimier properties exist for >, ≤ and ≥

11. L INEAR I NEQUALITY IN O NE V ARIABLE A linear inequality in one variable is an inequality that can be written in one of the following forms, where a ≠ 0: ax+b>0, ax+b<0, ax+b ≥0, ax+b ≤0

12. S OLVING L INEAR I NEQUALITIES Exercise: 1, 10x+5-7x ≥8(x+2)+4 2, (2x+3)/5-(3x-1)/2<(4x+7)/2

13. G RAPHICAL A PPROACHES f(x) < g(x) f(x) > g(x) f(x) ≤ g(x) f(x) ≥ g(x) f(x) g(x)

14. G RAPHICAL A PPROACHES X-Intercept Method of Solution of a linear Inequality The solution set of F(x)>0 is the set of all real numbers x such that the graph of F is above the x-axis. The solution set of F(x)<0 is the set of all real numbers x such that the graph of F is below the x-axis.

15. T HREE – P ART I NEQUALITIES Three – Part inequalities have the form of : ex: -3< 2x+1 < 2 x+1 < 3x+4 < 2x+6 g(x) < f(x) <h(x) g(x) ≤ f(x) <h(x) g(x) < f(x) ≤ h(x) g(x) ≤ f(x) ≤ h(x)

16. H OMEWORK PG. 57: 25-100 (M5) KEY: 30,70,85 Reading: 1.6 Linear Modeling