Unit 2 : One Variable Equations and Inequalities



Unit 2 : One Variable Equations and Inequalities

Class Notes Day 1 – Translating Sentences, 1-Step and 2-Step Equations

I. Definitions

Verbal Expressions Algebra Expressions Equations Variables

Formula / Literal Equations

II. Warm-up

1) The difference of twice a number x and 4 2) 3 times a number y less than twice the sum of a number x and 5

III. Translating Sentences into Equations - Practice

1) Five times the number a is equal to three times the sum of b and c.

2) Nine times y subtracted from 95 equals 37

3) The product of five and the sum of m and n is the same as seven times n.

4) Two times a number t decreased by 8 is identical to seventy.

5) Two hundred minus three times x is equal to nine.

6) the of twice r and three times s is identical to thirteen.

7) The sum of one-third q and 25 is as much as twice q

8) The square of m minus the cube of n is sixteen

9) Two times the sum of v and w is equal to two times z

IV Translate Sentences into Formulas

1) The are of a triangle is one-half the base of the triangle times the height

2) The Perimeter of a rectangle is equal to the sum of 2 times the length and 2 times the width

3) The Distance Formula is the square root of the entire quantity of the difference of x sub 2 and x sub 1 squared and the difference of y sub 2 and y sub 1

4) The volume of a rectangular prism is the same as the product of length, width and height.

5) The volume of a sphere is four-thirds times pi times the radius cubed

V. One Step Equations

Addition and Subtraction Equations: 1) [pic] 2) [pic]

3) [pic] 4) [pic]

Multiplication Equations: 5) [pic] 6) [pic]

Division Equations: 7) [pic] 8) [pic]

Practice:

9) [pic] 10) [pic] 11) [pic]

12) [pic] 13) [pic] 14) [pic]

15) [pic] 16) [pic] 17) [pic]

18) [pic] 19) [pic] 20) [pic]

VI. Two Step Equations

Multiplication: 1) [pic] 2) [pic]

3) [pic] 4) [pic]

Division: 5) [pic] 6) [pic]

7) [pic] 8) [pic]

Practice:

9) [pic] 10) [pic] 11) [pic]

12) [pic] 13) [pic] 14) [pic]

15) [pic] 16) [pic] 17) [pic]

18) [pic] 19) [pic] 20) [pic]

VII. HOMEWORK Solve each equation showing all steps.

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

16) [pic] 17) [pic] 18) [pic]

19) [pic] 20) [pic] 21) [pic]

22) [pic] 23) [pic] 24) [pic]

25) [pic] 26) [pic] 27) [pic]

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