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Algebra I
Chapter 3 Study Guide
Name: ________________________________________________
10/07/11
3.1/3.2: Solving one-step equations with addition/subtraction and multiplication/division
Know definitions of the following:
 Additive Inverse:
 Additive Identity:
 Multiplicative Inverse:
 Multiplicative Identity:
Examples of problems:

x – 10 = -4
x + 6 = -17
2x  24
5
x  30
6
3.3: Solving two-step equations
Examples of problems: Keep answers in fraction form where necessary.

3x + 10 = 31
15 – 6x = -9
2
(6x 18)  5  22
3
3
1
x6  x2
4
6
Word Problems: Define a variable, write an equation, and solve.
 Find three consecutive integers whose sum is 1,038.

Twenty-nine is 13 added to 4 times a number. Find the number.

A number is decreased by 35. Then multiplied by one-half. Then increased by 54. Then
divided by 11. The result is 4. What is the number?
3.4: Angles and Triangles in Algebra
Know definitions of the following:
 Complementary Angles:
 Supplementary Angles:
 Name triangles based on their sides:
 Name triangles based on their angles:
Examples of Complementary and Supplementary angles: Find each for the given angle.
 54
103
(x – 65) 
(y + 22) 
Word Problems: Define a variable, write an equation and solve.
 The measure of an angle is 43 greater than its complement. Find the measure of each
angle.

In an isosceles triangle, the vertex angle measures 37. What is the measure of the base
angles?

The angles of a triangle are given as 2x, (x – 12)  and (3x + 15)
3.5: Solving equation with variables on both sides.
Examples of problems: Keep answer in fraction form where necessary.

17 + 2n = 21 + 2n
2(x – 3) + 5 = 3(x – 1)
1
3(2n  5)  (12n  30)
2

7  3t t

4
8
-8(4 + 9x) = 7(-2 – 11x)
4m  5 m  2

6
5
Examples of word problems: Define a variable, write an equation and solve.
 Three times the greatest of three consecutive even integers is twice the least increased by
38. Find all of the numbers.

One half of a number increased by 16 is four less than two thirds of the number. Find the
number.
3.6: Solving an equation for a given variable.
Given the equation or formula, solve for the indicated variable.

ex  2y  3z , solve for x
by  2
 c , solve for y
3
c
3
y  2bm , solve for y
4
Word Problems: write an equation and solve for the specified variable.
 Four times a number x increased by 15 is 22 less than three fourths of a number y. Solve
for y.
Questions/Comments:
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