Algebraic Expressions and Equations Convert units of measurements Formulas Solving Inequalities Problem Solving.

Algebraic Expressions and Equations

Convert units of measurements

Formulas

Solving Inequalities

Problem Solving

Proportions Review

A car can travel 300 miles on 15 gallons of gas. How many gallons of gas are needed to travel 50 miles?

I can text 100 words in 4 minutes. How many minutes will it take me to text a message that has 1500 words?

P.56 # 1

p. 57 # 4 & 5

Convert between Metric and US

The SI unit is the international accepted model of measurement in the world. However, it is not utilized in the US.

p. 58 Charts the measurements and conversions.

a) Length

b) Capacity/Volume

c) Mass

Steps to change ……

Example 1: If a person is 140 centimeters tall, how many inches tall are they? (Round to two decimal places)

Know

Measurement given

Measurement desired

Example 2: Capacity/Volume

If Bill drank 4 quarts of water, how many liters is that?

Given 1 liter (L) = 1.057 quarts (qt) Plan:

Weight

If you had 1000 grams of sugar, how many ounces will that be?

Temperature

You have decided to go to Canada for the weekend and the meteorologist describes a brisk 4oC. Should you wear shorts or head back to Orlando?

Hint: F = 9/5 c + 32 or C = 5/9(F – 32)

Formulas

A list of formulas to remember and know

Shapes: rectangle (perimeter) P = 2L + 2W

Rectangle (area) A = lw

Triangle (area) A = ½ bh

Cylinder (Volume) V = πr2h

Money: Sale = Original – discount

Interest = (Principal)(Interest Rate)(Time)

Manipulating Formulas

Solving in terms (explicitly) for a variable refers to isolating the variable in question.

Example: solve for w

A = lw to get w by itself we need to remove the l

A/l =lw/l Then divide/cancel the variable.

A/l = w

Practice

Solve for h given V = πr2h What is the arithmetic relationship between pi,

r and h? How do we undo the operation Solve

p. 66 and 67 #1, 4, 7,9

Inequalities

Symbol Terms/Words

< is less than

< is less than or equal to

no more than

> Is greater than

> is greater than or equal to

at least

Graphing Inequalities

X < 3 means all numbers that are smaller than 3 but does not include 3

Y > -1 all numbers greater than –1 and including –1

P.69

Solving Inequalities

The objective in algebra is always to isolate or define the unknown variable.

To solve for an inequality we need to move the numerical value to one side of the inequality and the variable to the other side.

Solve for x: 10 – 2x > 15

10 – 2x > 15

Solve for 6x – 8 < 8x + 10

6x – 8 < 8x + 10

Solving compound inequalities

Solve the same as one inequality, but apply the steps for both sides

-5< x + 4 < 14

p.72 Example 3p.73-74

Applications

READ, READ, READ Circle/highlight the question What are key words (underline, highlight,

circle) Determine plan to solve the problem Test or solve Check the numerical result with the question.

Does it make sense?

A pair of jeans is priced at $50, but is on sale for 25% off. What is the sale price of the jeans? What do we want to solve for? What does the first number represent? What is the second number? How to approach or solve? Does the answer describe what is asked for?

What amount should I invest at 5% simple interest to yield $200 in interest in 8 years? I = PRT What is the unknown variable in the problem?

Problem solving

Practice problems p.77