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Unit 2 Test Review! . 7 th Grade Pre-Algebra 2013-2014 Ms. Beaty. An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: . is less than. Fewer than, below. is greater than. More than, above.

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Unit 2 test review

Unit 2 Test Review!

7th Grade Pre-Algebra

2013-2014

Ms. Beaty


An inequalitystates that two quantities

either are not equal or may not be

equal. An inequality uses one of the

following symbols:

is less than

Fewer than, below

is greater than

More than, above

is less than or equal to

At most, no more than

is greater than or equal to

At least, no less than


Graphing inequalities
Graphing inequalities

  • When a number is greater than or less than, you used an open dot on the graph.

    • I think of the dot as being empty. It does not contain the number it is on.

  • When a number is greater than or equal to or less than or equal to, you use a closed dot.

    • I think of the dot as being full. It contains the number it is on.


Let s try one
Let’s try one!!!

3 + x < 9

WAIT!

The x is not isolated yet! What do we do??

That’s right! We do the inverse to isolate the variable. It’s the same way you have been solving the equations.


Let s try it again
Let’s try it again!

  • 3 + x < 9

  • Isolate the variable by undoing the constant. Subtract 3 from both sides and you’re left with:

    x < 6

  • This would read x is less than 6. This means that x can be any number less than 6.

  • In order to represent this, we put it on a graph.


Graphing the inequality
Graphing the inequality

  • x < 6

  • Why did we use an open dot?

  • Why did the arrow point to the left?

3 4 5 6 7 8 9 10


Let s try a few more
Let’s try a few more!

  • X> 4.5

  • X < -3

  • X < -17

  • X > 4


Lets try inequalities with words
Lets try inequalities with words!

  • All real numbers less than 5

  • All real numbers greater than -1

  • All real number less than or equal to ½

  • All real number greater than or equal to 0


Write an inequality for the situation.

There are at most 87 people in the school.


Write an inequality for the situation.

At least 31 pencils are on the tray.


Additional Example 3: Money Application

Edgar’s August profit of $137 was at least $20 higher than his July profit. What was July’s profit?

Let p represent the profit increase from July to August.

August profitwas at least$20 higher thanJuly’s profit.

$137≥ 20 +p

137 ≥ 20 + p

Subtract 20 from both sides.

-20 -20

117≥ p

p ≤ 117

Rewrite the inequality.

July’s profit was at most $117.



y

2

– 6 > 1

y

2

> 7

y

2

> (2)7

(2)

Additional Example 1A: Solving Two-Step Inequalities

Solve. Then graph the solution set on a number line.

y

2

– 6 > 1

+ 6 + 6

Add 6 to both sides.

Multiply both sides by 2.

y > 14


Additional Example 1C: Solving Two-Step Inequalities

Solve.

4y – 5 < 11

4y – 5 < 11

+ 5 + 5

Add 5 to both sides.

4y < 16

4y < 16

Divide both sides by 4.

4

4

y < 4


12

252

, or 12

r ≤

Additional Example 2: Application

Sun-Li has $30 to spend at the carnival. Admission is $5, and each ride costs $2. What is the greatest number of rides she can ride?

Let r represent the number of rides Sun-Li can ride.

5 + 2r ≤ 30

– 5 –5

Subtract 5 from both sides.

2r ≤ 25

Divide both sides by 2.

2r ≤ 25

2 2

Sun-Li can ride only a whole number of rides, so the most she can ride is 12.


Check It Out: Example 2

Brice has $30 to take his brother and his friends to the movies. If each ticket costs $4.00, and he must buy tickets for himself and his brother, what is the greatest number of friends he can invite?

Let t represent the number of tickets.

8 + 4t ≤ 30

– 8 –8

Subtract 8 from both sides.

4t≤ 22

Divide both sides by 4.

4t≤ 22

4 4

t ≤ 5.5

Brice can only buy a whole number of tickets, so the most people he can invite is 5.


Combining like terms
Combining Like Terms

  • Must have the same:

    • Variable (Letter)

    • Exponent (Power)

      • Example:

      • (2a + 3) + (a +7)


Steps for solving a 2 step equation
Steps for Solving a 2-Step Equation.

  • Our Goal: Isolate the Variable!

    • 1. Draw your slide to line up the equal signs.

    • 2. Undo the constant by using the inverse operation.

    • 3. Undo the variable term by using the inverse operation

    • 4. Write the solution.


4 x 2 38
4x + 2 = 38


What if there are two variable terms
What if there are two variable terms?

  • 2a = 7a +40

    -7a -7a

    -5a = 40

    -5 -5

    a = -8

  • 1. Get the variable terms on one side, and constants on the other.

  • Use inverse operation to isolate the variable.



Look for key words and translate them into mathematic symbols
Look for key words and translate them into mathematic symbols.

  • Special cases

    • More than: addition expression with the terms swapped

    • Less than: subtraction expression with the terms swapped

    • Divided into: division expression with the terms swapped



  • Syreeta cost an additional $0.15 each. If Luis’s cell phone bill last month totaled $55.05, write and solve an equation to determine how many text messages he sent. wants to buy some CDs that each cost $23. She has $65. Write and solve an equation to find how many CDs she can buy.


  • Toya cost an additional $0.15 each. If Luis’s cell phone bill last month totaled $55.05, write and solve an equation to determine how many text messages he sent. had her birthday party at the movies. IT cost $27 for pizza and $8.50 per friend for the movie tickets. How many friends did Toya have at her party if she spent $78.





  • Doritos are on sale at Kroger. If Ms. the price of each item if the ticket cost 3 times as much as the popcorn?Beaty buys 3 bags, it will cost her $6. If she buys them individually, she has to pay $3.99 each. How much money will she save on each bag if she buys 3.


  • Ms. the price of each item if the ticket cost 3 times as much as the popcorn?Beaty can buy a Blu-Ray player for $45 and rent redbox movies for $10 a month or she can use her laptop and stream netflix for $15 per month. How many months would she need to stream netflix to pay as much as she would if she had bought the Ble-Ray and rented redbox movies?





  • Ms. fee of $60.00, as well as $9.75 each day. Her total cost was $138.00. For how many days did she rent the car?Beaty found a Braves shirt that she wants to buy for her little brother’s birthday. The original price is $25. It is currently on sale at 15% off Ms. Beaty also has a $5 coupon. How much will the shirt cost before tax?






  • E in Dallas, the low temperature was rin spent $12.25 on supplies to make lemonade. At least how many glasses of lemonade must she sell at $0.30 per glass to make a profit?



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