More "And" "Or" Inequalities

More "And" "Or" Inequalities

Algebra I

Warm-Up!

Answer the review questions on the next three slides before starting the lesson.

Multiple Select

Which value(s) make the following equation true? Select all that apply.

 $w^2=121$  

• 11

• 60.5

• -11

• -60.5

• 123

Multiple Choice

Match the correct graph to the story below.

A plumber charges a fixed fee for coming to your house, then charges a fixed amount on top of this.

x = the time the job takes in hours

y = the total cost of the plumber's time in dollars

Multiple Choice

Write as a trinomial

 $\left(3x-10\right)\left(x-2\right)$  

•  $3x^2-16x+20$  

•  $3x-16x+20$  

•  $3x^2-12x-20$  

•  $3x^2+16x-20$  

 $-5<x<4$  

•  $-5<x$ , which is equivalent to  $x>-5$   

•  $x<4$  

• This means that x is any value between -5 and 4, not including -5 or 4

• The solution set is graphed to the right

Multiple Choice

What does an open circle indicate when graphing an inequality?

• The value is an answer in the solution set.

• The value is not an answer in the solution set.

Example 1: AND

 $-5<2x+1<4$  

• Rewrite the inequality as a compound statement of inequality

• Solve each inequality for x

• Write the solution to the compound inequality

• Graph the solution set on the number line

Example 2: OR

 $x+4<6$ OR $x-1>3$   

• Solve each inequality for x

• Write the solution of the compound inequality

• Graph the solution set on the number line

 $x-1>-1$  and  $x+6<8$ 

Through the next few slides, you will work through the inequality above, step-by-step.

Multiple Choice

Solve the first inequality.

 $x-1>-1$  and $x+6<8$  

•  $x>-2$  

•  $x\ ≥\ 0$  

•  $x<0$  

•  $x>0$  

Multiple Choice

Solve the second inequality.

 $x-1>-1$  and $x+6<8$  

•  $x<14$  

•  $x\ <48$  

•  $x<2$  

•  $x>0$  

Multiple Choice

Write as a compound inequality.

 $x-1>-1$  and $x+6<8$  

•  $0<x<2$  

•  $2<x<0$  

•  $0\ ≤ x<2$  

•  $-2<x<0$  

Multiple Choice

Graph the solution set.

 $x-1>-1$  and $x+6<8$  

 $x-1>-1$  and $x+6<8$  

The image to the right shows how to solve the previous question in one picture.

Example 3

 $-1\ ≤ 3-2x\ ≤ 10$  

• Rewrite the inequality as a compound statement of inequality

• Solve each inequality for x

• Write the solution to the compound inequality

• Graph the solution set on the number line

Multiple Choice

When solving an inequality for its solution set, when do you flip the inequality symbol?

• Never

• When multiplying or dividng by a negative

• When adding or subtracting a negative

• When multiplying or dividing by any number

Multiple Choice

 $5x+1<0$  or  $8\ ≤\ x-5$  

Solve the compound inequality for the solution set.

•  $x<-\frac{1}{5}$  or  $x\ ≥ 13$  

•  $x<-5$  or $x>13$  

•  $x<\frac{1}{5}$  or $x\ ≥\ 13$  

•  $x>-\frac{1}{5}$  or $x\ ≤\ 13$  

Multiple Choice

 $x-2\ ≤ 4$  and  $x-2\ ≥ 4$  

Solve the compound inequality for the solution set.

• 
   $x=-6$ 

•  $x=6$  

•  $x\ ≠\ 6$  

Example 4

 $5x\ ≤ 21+2x$  or $3\left(x+1\right)\ ≥ 24$  

• Rewrite the inequality as a compound statement of inequality

• Solve each inequality for x

• Write the solution to the compound inequality

• Graph the solution set on the number line

The End

Transition over to today's Google Doc assignment.