Algebra Chapter 9.1-9.3 Review

Algebra Chapter 9.1-9.3 Review

Inequalities and Problem Solving

Solving Inequalities

• Inequalities can be solved graphically

• First, look at the graph of the two functions

• Second, determine the x-values where one graph lies above the other

Solving Inequalities

Since the graph of g(x) is above the graph of f(x) after x=2, the solution of g(x)>f(x) is {x|x>2}

Multiple Choice

Solve graphically:
 $2x-5\ge\frac{1}{2}x+1$  

•  $x\ge5$  

•  $x\ge6$  

•  $x\ge4$  

•  $x\ge1$  

Intersections

• A conjunction is when two or more sentences are joined by the word and

• The solution to a conjunction is the intersection of the solution sets

• Or only the elements that both sets share

Intersections

• We first separate the inequality into two separate inequalities

• Then, we solve for both inequalities

• We can write our answer using set-builder notation or interval notation

Multiple Choice

Click on the picture to enlarge it.

• $\left(-2,\ -\frac{3}{4}\right]$

• $\left(-4,\ -\frac{7}{4}\right]$

• $\left(-5,\ -\frac{4}{3}\right]$

• $\left(-5,\ -\frac{7}{4}\right]$

Unions

• A disjunction is when two or more sentences are joined by the word or

• The solution set of a disjunction is the union of the solution sets

• Or all the elements in both sets

Unions

• We first separate the inequality into two separate inequalities

• Then, we solve for both inequalities

• We can write our answer using set-builder notation or interval notation