Compound Inequalities, Isolating Variables, Graphing Lines

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.

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