Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1.5 LINEAR EQUATIONS AND INEQUALITIES QUIZ Tell true or false of the following statement: If c < 0, a < b, then ac > bc. LINEAR EQUATION A linear equation in one variable is an equation that can be written in the form: ax+b=0, a≠0 LINEAR EQUATION 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. SOLVE 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) SOLVE A LINEAR EQUATION BY GRAPH To solve the equation f(x)=g(x) graphically, graph y1 =f(x) and y2=g(x) The x-coordinate of any point of intersection of the two graphs is a solution of the equation. SOLVE A LINEAR EQUATION BY GRAPH X-Intercept Method of Graphical Solution To solve the equation f(x)=g(x) graphically, graph y =f(x) -g(x)=F(x) 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. IDENTITIES AND CONTRADICTIONS 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 INEQUALITIES IN ONE VARIABLE Notation: a<b a>b a≤b a≥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 ADDITION AND MULTIPLICATION PROPERTIES OF INEQUALITY For real numbers a, b and c 1, if a < b, then a + c < b + c. 2, If a < b, c > 0, then ac < bc 3, if a < b, c < 0, then ac > bc Slimier properties exist for >, ≤ and ≥ LINEAR INEQUALITY IN ONE VARIABLE 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 SOLVING LINEAR INEQUALITIES Exercise: 1, 10x+5-7x ≥8(x+2)+4 2, (2x+3)/5-(3x-1)/2<(4x+7)/2 GRAPHICAL APPROACHES f(x) f(x) < g(x) g(x) f(x) > g(x) f(x) ≤ g(x) f(x) ≥ g(x) GRAPHICAL APPROACHES 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. THREE – PART INEQUALITIES Three – Part inequalities have the form of : g(x) < f(x) <h(x) g(x) ≤ f(x) <h(x) g(x) < f(x) ≤ h(x) g(x) ≤ f(x) ≤ h(x) ex: -3< 2x+1 < 2 x+1 < 3x+4 < 2x+6 HOMEWORK PG. 57: 25-100 (M5) KEY: 30,70,85 Reading: 1.6 Linear Modeling