Absolute Values

Is its distance from zero, not its value.

1-31= 3

Because both units are three units away from zero.

Inequalities

Look like equations, except that instead of having an equal sign, they have one of the following symbols:

> greater than

< less than

>greater than or equal to

< less than or equal to

PEMDAS

1. Parentheses

2. Exponents
3. Multiplication
4. Division
5. Addition

6. Subtraction

A fence measures 15 ft. Long. How many yards long is the fence?

1 yd. = 3 ft

15/3 = 5 yd

A pitcher can hold 24 cups. How many gallons can it hold?

1 gal. = 16 cups

24/16 = 1.5 gallons

A spoil of wire holds 144 in. Of wire. If Mario has 3 spools, how many feet of wire does he have?

12 inches = 1 ft.

144/12 = 12 ft.

12 ft. x 3 spools = 36 ft. Of wire

A ball rolling across the table travels 6 inches per second. How many feet will it travel in 1 minute?

1 minute = 60 seconds

(6 in.)/(sec.) x 60 s = 360 in.

1 ft. = 12 inches

(360            in.) = 30 ft.

How many millimeters are in 0.5 m?

meter = 1000 mm

0.5 = 500m

 

A lead ball weighs 38 g. How many kilograms does it weigh?

1 kg = 1000 g

38/1000g = 0.038 kg

How many cubic centimeters are in 10 L?

1 L = 1000 ml

10 L = 1000 ml x 10

10 L = 10,000 ml or cm3

The pencil was initially 10 centimeters long. After she sharpened it, it was 9.6 centimeters long. How many millimeters did the pencil lose by sharpening it?

1 cm = 10 mm

10 cm – 9.6 cm = 0.4 cm lost

0.4 cm = 10 x .4 = 4 mm were lost

A sporting goods store is offering an additional 30% off all clearance items. Angie purchases a pair of running shoes on clearance for $65.00. If the shoes were originally $85.00, what was the total discount?

$65.00 x 70/100 = $45.50 $45.50/$85.00 = WI 00

x =  = 53.5

 

Angie is paying 53.5% the original price, which means she received a 100%-53.5%=46.5% discount.

If a discount of 25% off the retail price of a desk saves Mark $45, what was the desk’s original price?

 

(25/100) X x = $45 (25% of x equals $45)

X = 45/0.25 –> $180

What number is 5% of 2000?

2000 x 0.05 = 100

Solve for x and y:

15x+2y=3 and 12x+y=-3

2(12x+y=-3) –> 24x+2y=-6

15x+2y=3 – (24x+2y=-6) = -9x = 9

Next divide by 9 to solve for X:
5y/5 = -30/5 should be -9x/9 = 9/9
X= -1

Then plug this value into another equation to solve for y:
15(-1) + 2(y) = 3
2y= 18
Y=9

If |3x+2| = 5

+ (3x + 2) = 5 or -(3x + 2) = 5

3x = 5 – 2 or -(-3x + 2) = 5

X = 1 or -7/3

Therefore, (1, -7/3).