Compound Inequalities and Interval Notation

Reviewing Compound Inequalities, Isolating Variables, and Graphing Lines  

Happy Monday!  Let's review some ideas from the last few weeks :)

Review of Compound Inequalties

This topic will come up again this week.

Multiple Select

$$4\le x\le10$$  

Check all that are true regarding this compound inequality.

• This is an "AND" type question

• This is an "OR" type question

• The graph will look like oars on a boat (kick out to the sides)

• The graph will shade in between the values.

• The values of 4 and 10 will have brackets on them.

Multiple Choice

What is the correct inequality notation for this graphed solution?

• $$x<-3\ or\ x>-2$$

• $$x>-3\ or\ x<-2$$

• $$x\le-3\ or\ x\ge-2$$

• $$x<-3\ and\ x>-2$$

• $$x>-3\ and\ x<-2$$  

Multiple Choice

What is the correct interval notation for this graphed solution?

• $$\left(-3,2\right)$$

• $$\left(-\infty,-3\right)\cup\left(-2,\infty\right)$$

• $$\left(-\infty,-3\right]\cup\left[-2,\infty\right]$$

• $$\left[-3,-2\right]$$

Review of Isolating Variables

This topic will come up again this week.

Multiple Choice

When trying to solve for y, which of the following should be the first step?

$$3x+4y=8$$  

• $$7y=8$$  

• $$4y=-3x+8$$  

• $$4y=3x+8$$  

• $$x+\frac{4}{3}y=\frac{8}{3}$$  

Multiple Choice

What is the NEXT correct step in the following question when isolating for y:

$$xy+5y=9$$  

• $$5xy=9$$  

• $$5y=9-xy$$  

• $$y\left(x+5\right)=9$$  

Let's review graphing lines!

Again, we will be revisiting this skill this week.

Fill in the Blanks

The slope of the given line is

 

$y=-\frac{3}{4}x+7$  

Multiple Select

When graphing the given line, which of the following are TRUE?  

Check ALL that apply!

$$y=-\frac{3}{4}x+7$$  

• Start by marking a point at $$\left(0,7\right)$$  

• Start by marking a point at   $$\left(7,0\right)$$  

• To create a second point, move up 3 and right 4

• To create a second point, move down 3 and right 4

• You need to graph at least 2 points to make a line.

Multiple Choice

Which of the following is a VERTICAL line?

• $$y=3x$$

• $$x=3$$

• $$y=3$$

• $$x=3y$$

Now Put Those Concepts Together!

In this week, we will need to graph lines to solve systems, and sometimes the equation is not in slope-intercept form.

Multiple Choice

What is the slope of the given equation?

$$4x+3y=9$$  

• $$\frac{4}{3}$$  

• $$3$$  

• $$-\frac{4}{3}$$  

• $$-\frac{3}{4}$$  

• $$3$$  

Multiple Choice

What is the y-intercept of the given equation?

$$4x+3y=9$$  

• $$-\frac{4}{3}$$  

• $$3$$  

• $$4$$  

• $$9$$  

A Preview to an Upcoming Lesson

Solving Systems by Graphing