Equations and Inequalities Reteach-Retake Day 3

Equations and Inequalities Reteach-Retake Day 3

Today should be easier than yesterday!

Inequalities are similar and different from equations

We (mostly) solve them the same way.

BUT they have infinitely many solutions. That's why their "answer" is a graph instead of a number.

Basic Inequalities

Think of a number greater than 1. There are an infinite number of possibilities.

Graphing the solutions

The infinite solutions to inequalities are represented on a number line. The starting point of the ray is either included or excluded.

Number Line Graphs

1. x is more than 3 (can't =3)

2. x is less than 3 (can't =3)

3. x is at least 3 (3,4,5,6...)

4. x is at most 4 (4,3,2,1,0,...)

Solve Inequailites like Equations, BUT

If you divide or multiply by a negative number, reverse the <>

If we don't, the inequality won't be true anymore. It has to do with negative meaning "Opposite."

Multiple Choice

Solve by isolating the variable.

 $3x\ge12$  

•  $x\ge4$  

•  $x\le4$  

Multiple Choice

Solve the inequality by isolating the variable.

 $-3y\le12$  

•  $y\le-4$  

•  $y\ge-4$  

Multiple Choice

How would you solve this inequailty? Would you flip the sign?  $\frac{a}{2}\ge-10$  

• Multiply both sides by 2; yes flip the sign.  $a\le-20$  

• Multiply both sides by 2; no, don't flip the sign.  $a\ge-20$  

Multiple Choice

 $7+y<10$  

How would you solve the inequality? Would you flip the sign?

• Subtract 7 from both sides. No, don't flip the sign.  $y<10$  

• Subtract 7 from both sides. Yes, flip the sign.  $y>10$  

Open Ended

 $-5\ge z$  

Type in some numbers that satisfy the inequality. (What could z be? Type more than one)

Poll

Consider this inequality word problem. Which statement(s) do you agree match the situation?

You must be at least 48 inches to ride the roller coaster at the state fair.

• x can be 48 inches or taller than that.

• $x\le48$

• $x\ge48$

• x can be no taller than 48 inches

Please return to the live lesson room.

I will show you some examples of equation and inequality word problems before you will try on your own.

Multiple Choice

You have $59.95 in your wallet and want to buy some new CDs. If the CDs are $11.99 each, what number of CDs, x, can you buy?

What is "each" a keyword for?

• addition

• subtraction

• multiplication

• division

Multiple Choice

You have $59.95 in your wallet and want to buy some new CDs. If the CDs are $11.99 each, what number of CDs, x, can you buy? Which statement matches the situation?

• $11.99x\ge59.95$

  you can spend more than $59.95 on the CDs

• $11.99x\le59.95$ you can spend 59.95 or less on the CDs

• $11x<59.95$ you can spend less than $59.95 on the CDs

Multiple Choice

 $11.99x\le59.95$  

Solve the inequality. Use a calculator!

•  $x\ge5$  

•  $x\le5$  

Multiple Choice

What would you do first to solve

 $5\left(2x-1\right)=-35$  

• Distribute! You would get 10x-10=-35

• Add 5 to both sides. You would bet 2x-1=-30

• Subtract 5 from both sides. You would get 2x-1=-40

Multiple Choice

What would you do first to solve

 $4x-10=2x+4$  

• Combine the 4x and 2x to get 6x-10=4

• Subtract 10 and 4 to get 6=2x+4

• Subtract 2x from both sides to get 2x-10=4. 

Open Ended

How was this three day reteach-retake? What should I do differently next semester?