9/15 Digital Learning Day ACC

Digital Learning Day 9/15

7th Grade ACC Math

Take your time to watch videos, read slides, and write your work out. Don't forget your rules for solving equations.
Don't forget when you multiply or divide by a negative, you must flip the inequality symbol.

Inequalities

What is an inequality?

Review:

Equations (means-equal)

Remember when we solved equations we isolated the variable on one side by using inverse operations. You will solve inequalities the same way you solve equation. The only difference in them will be the symbol used.

How are equations and inequalities different?

Equations

Have an = sign

Only have one answer when solved

Inequalities

Don't have and = sign instead use inequality symbols

< (less than)

> (greater than)

≤ (less than or equal to)

≥ (greater than or equal to)

Can have multiple answers when solved

Example of an inequality and how to interpret your answer.

Multiple Choice

Solve the following inequality:

x + 2 > 12

• subtract 2 from both sides and your answer is

  x = 10

• subtract 2 from both sides and your answer is

  x > 10

• subtract 2 from both sides and your answer is

  X < 10

Multiple Choice

Solve 5x > 10

• divide by 5 on both sides and your answer is

  x = 2

• divide by 5 on both sides and your answer is

  x < 2

• divide by 5 on both sides and your answer is

  x > 2

Multiple Choice

Solve 3x + 2 > 8

• subtract 2 from both sides and your answer is

  x > 6

• subtract 2 from both sides and your answer is

  x = 6

• subtract 2 from both sides and then divide by 3 on both sides and your answer is

  x > 2

Multiple Choice

Solve the inequality

3x - 7 < 5

• x < 4

• x < -2

• x = 4

One Rule: If you are multiplying or dividing by a negative number you must switch the direction of the inequality symbol. 

• (ex) Solve -4x > -12

• Divide both sides by -4, and because we are dividing by a negative number, we must reverse the inequality sign

  ⇒ -4x/-4 < -12/-4

  ⇒ x < 3

Multiple Choice

Try some:

-2x ≤ 4

• divide by -2 o both sided and your answer will be

  x = -2

• divide by -2 on both sides and you will switch the direction of the inequality since you are dividing by a negative and your answer will be

  x ≥ -2

• divide by -2 on both sides and your answer will be

  x ≤ -2

Multiple Choice

- 3x < -12

• divide both sides by -3 and your answer is

  x < 4

• x = 4

• divide both sides by -3 and your answer is

  x > 4

  because you divided by a negative and had to flip the inequality symbol

Multiple Choice

Example

$$\frac{x}{-2}\ge3$$

• multiply both sides by -2 and your answer will be

  x ≤ -6

  because you multiplied by a negative you must switch the inequality

• multiply both sides by -2 and your answer will be

  x ≥ -6

• divide both sides by -2 and you get

  x ≥ -2/3

GREATER THAN

• is greater than

• is more than

LESS THAN

• is less than

• is fewer than

GREATER THAN OR EQUAL TO

• is greater than or equal to

• is at least

• is no less than

LESS THAN OR EQUAL TO

• is less than or equal to

• is at most

• is no more than

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

There are fewer than 50 people allowed in this area.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I need at least 30 orders to meet my qouta.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I see more than a dozen seagulls.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I can spend no more than $20 at the store.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

Each gumball in a gumball machine costs $0.25. You can spend no more than $2.50 in total on gumballs.

Which inequality would represent how many gumballs you could buy?

• $$0.25x\ <\ 2.50$$

• $$0.25x\ >\ 2.50$$

• $$0.25x\ \le\ 2.50$$

• $$0.25x\ \ge\ 2.50$$

Multiple Choice

You have $30 to buy baseball cards. Each pack of cards costs $5. Write an inequality that represents the number of packs of baseball cards you can buy and still have at least $10 left.

• $$30\ -\ 5x\ \ge10$$

• $$30\ -\ 5x\ \le\ 10$$

• $$30\ -\ 5x\ <\ 10$$

• $$30\ -\ 5x\ >\ 10$$

GRAPH OF AN INEQUALITY

Multiple Choice

WHICH INEQUALITY IS REPRESENTED BY THE GRAPH?

• $$X\ <\ 1$$

• $$X\ \le\ 1$$

• $$X\ >\ 1$$

• $$X\ \ge\ 1$$

Multiple Choice

WHICH INEQUALITY IS REPRESENTED BY THE GRAPH?

• $$X\ <\ 2$$  

• $$X\ \ge\ 2$$  

• $$X\ >\ 2$$  

• $$X\ \le\ 2$$  

Compound Inequalities

AND vs OR

• Compound Inequalities have two inequalities attached to each other and mean that both statements are true.

• When you graph an AND inequality, the arrows will point to each other.

• When you get an OR inequalities, the arrows will point away from each other

AND

Here is a video on how to solve a Compound Inequality that uses the word AND.

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$4\le x+2\le8$$  ?

Correct Answer

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$-9<x-10<5$$  ?

Correct Answer

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$-50<7x+6<-8$$  ?

Correct Answer

This one requires two steps.

OR

Here is a video on how to solve a Compound Inequality that uses the word OR.

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$2+r<12$$  or  $$r+5>19$$  

Correct Answer

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$7x\ge21$$  or  $$2x\le-2$$  

Correct Answer

Now here are some problem with BOTH types of Compound Inequalities

You will have to recall which is which.

And some with have multiple steps to solve.

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$-5x+2>27$$  or  $$x-3>2$$  

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$-18<3x-6\le-3$$  

Multiple Choice

Which compound inequality is represented in the graph?

• $$-2\le x<5$$

• $$-2<x\le5$$

• $$x\ge-2$$ or $$x>5$$

• $$x<5$$ or $$x\le-2$$

Multiple Choice

Which compound inequality is represented in the graph?

• $$x\le10$$  or  $$x>17$$  
  

• $$x\ge10$$  or  $$x<17$$  
  

• $$10\le x<17$$  

• $$10\le x\le17$$  

• $$x\le10$$  or  $$x<17$$  

Multiple Choice

The statement “x ≥ 4 and 2x - 4 < 6” is true when x is equal to...

• 1

• 10

• 5

• 4

• 20

Multiple Choice

In order to be admitted for a certain ride at an amusement park, a child must be greater than or equal to 36 inches tall and less than 48 inches tall. Which graph represents these conditions?

Literal Equations

These are also known as "multi-variable"

In these problems you will have to follow the same rules as solving equations, but you will only have letters. Please watch the following 2 minute video to get a quick overview.

Multiple Choice

What is the first step in solving this equation for b?

$$A\ =\ bh$$  

• Subtract h from both sides.

• Divide by h on both sides.
  

• Add h to both sides.

• Multiply by h on both sides.

Multiple Choice

Solve for F.

$$S=3F-24$$  

• $$F=\frac{\left(s+24\right)}{3}$$  

• $$F=3S+24$$  

• $$F=\frac{S}{3}+24$$  

• $$F=3\left(S+24\right)$$  

Multiple Choice

Solve for x.

$$x+2w=m$$  

• $$x=m-2w$$  

• $$x=2mw$$  

• $$x=0.5m-w$$  

• $$x=\frac{m}{2w}$$  

Multiple Choice

Solve for r.

$$C=2\pi r$$  

• $$\frac{C}{2\pi}=r$$  

• $$C\ +2\pi=r$$  

• $$C-2\pi=r$$  

• $$2\pi C=r$$  

Multiple Choice

Solve for W.

$$A=LW$$  

• $$A=\frac{L}{W}$$  

• $$W=A$$  

• $$W=\frac{L}{A}$$  

• $$W=\frac{A}{L}$$  

Multiple Choice

pV = nRT
solve for R

• R= pV/nT

• R= p/n + V/T

• R= pV - nT

• R= (pV-n)/T

Multiple Choice

Solve the literal equation for the given variable.

• 2A/h

• 2/(h)

• 2Ah

• Ah/2

Multiple Choice

Solve for A

$$\frac{a}{b}=h$$  

• $$a=bh$$  

• $$a=\frac{b}{h}$$  

• $$a=\frac{h}{b}$$  

Multiple Choice

$$V=lwh$$  solve for h

• $$h=Vlw$$  

• $$h=\frac{l}{Vw}$$  

• $$h=\frac{V}{lw}$$  

• $$h=\frac{w}{lV}$$  

Let us use the distributive property with Literal equations to solve for X.

Notice we start simplifying like any other equation, but end up with

AX-2X=5B. We want only one X, and AX and -2X and not like terms. We can use the distributive property to factor out the X. Now we have one X and can solve for X. try one.