Equations, Section 1.4, 1.5, 1.6

Gautier/Finizio

Period 1

Quiz Date: 9/23/05

Algeo 1

Equations, Section 1.4, 1.5, 1.6

Study Guide

Solving Equations

Sample Problem:

Step #1:

Isolate the 6x. In order to do this you must do the opposite operation. Therefore you will add 5 to BOTH sides of the equation.

Step #2:

Complete your additions or subtractions. -5 + 5 = 0, therefore you are left with 6x on the left side of the equation.

6x = 24

Step #3:

Isolate the X. In this equation it says 6 times X. In order to isolate the X you must perform the opposite operation (division) on BOTH sides of the equation.

The sixes on the left side of the equation cancel out and you are left with X alone.

Sample Problems:

Section 1.4: Translating words into Symbols

Other Important Information

Half of a Number =

Twice a Number =

Quantity Means Parenthesis

Sample Problems:

1. Four More than a Number =
2. Five Subtracted from a Number =
3. Seven Less than a Number =
4. Eight times the sum of a number and ten =

Practice Problems:

Translate Each Phrase into an Algebraic Expression.

1. Eight times a number
2. Five more than a number
3. A number decreased by four
4. Nine less than half a number
5. Nine more than twice a number
6. Seven decreased by three times a number
7. Five less than a number
8. Six more than half a number.

Translating Sentences into Equations

Use the same chart as in the above section. The only difference is that the word “IS” means that you need an EQUAL sign.

Sample Problems:

Three less than a number x is 12 =

One half of a number is 4 =

Five less than twice a number is 15 =

Practice Problems:

Translate each sentence into an equation.

1. Three more than a number is eight.

1. Twelve more than a number is 15.

1. The number a increased by 23 is 83.

1. The quotient of the number b and 4 is 8.

1. The product of 12 and the quantity 1 less than the number d is 84.

1. The sum of 3 and the number s is 23.

1. Three less than twice a number is eight.

Section 1.6: Translating Problems into Equations

Sample Problem:

Translate the following problem into an equation.

1. Marta has twice as much money as Heidi.
2. Together they have $36.

Let x = the amount of money that Heidi has.

Let 2x = the amount of money that Marta has.

Practice Problems

*Translate Each Problem into an Equation*

1.

a. Luke has $5 more than Sam.

b. together they have $73.

How much money does each have?

2.

a. Lisa walked 8 km more than Tim.

b. Lisa walked twice as far as Tim.

How far did each walk?

3.

a. Lyn has twice as much money as Jo.

b. Together they have $63.

How much money does each have?

4.

a. State College has 620 students

b. there are 20 more women than men.

How many women are there?