R.6 Solving 1-Variable Equations (Part 2)Name:
● Recall – Writing Algebraic Expressions.
Match the phrase with the correct algebraic expression. The expressions will be used more than once.
A. y – 2 B. 2yC. y + 2D. E. 2 – y
1. 2 more than y / 5. the quotient of y and 2 / 9. y decreased by 22. half of y / 6. y increased by 2 / 10. y doubled
3. 2 less than y / 7. 2 less y / 11. 2 minus y
4. twice y / 8. the product of 2 and y / 12. the sum of 2 and y
Writing algebraic equations
1. Triple the original number x is equal to 700. ______
2. The product of a number x and 5 is 15. ______
3. Four times the difference of a number x and 2 the same as is 20. ______
4. Seventeen more than half a number x is 35. ______
5. Four times the sum of a number x and 10 isidentical to 48. ______
Writing algebraic equations from situations
6. The number of parts in inventory, p, minus 54 parts sold is 320. ______
What does p represent in the equation? ______
7. One hundred seeds divided by 5 rows equals , s, number of seeds. ______
What does s represent in the equations? ______
8. His base pay of $200 increased by his commission, c, is $500. ______
What does c represent in the equation? ______
9. We started with s number of students. When 5 moved away, we had 12 students left. ______
What does s represent in the equation? ______
Writing equations from word problems
10. When 6 is added to four times a number, the result is 50. What is the number?
a. Define a variable for the unknown value. Let _____ represent ______
b. Write and solve the equation.c. Answer the question with the correct units.
11. On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two
grades was 138. What was the lowest grade?
a. Define a variable for the unknown value. Let _____ represent ______
b. Write and solve the equation.
c. Answer the question with the correct units.
12. In a given amount of time, Jamie drove twice as far as Rhonda. Altogether they drove 90 miles. Find the
number of miles driven by each.
a. Define a variable for the unknown value. Let _____ represent ______
b. Write and solve the equation.
c. Answer the question with the correct units.
●Solving Equations – Variable on Both Sides
Example 1:a. 3x + 2 = –2x – 8 b.8x – 7 = 7x – 2c. –x – 11 = 2x+ 4
● Solving Multi-StepEquations – Simplify each side by Combining Like Terms on each side.
Example 2: a. x – 1 + 5x = 23b. –28 + 15 – 22x = 31
c. 42x + 18 – 19x = –28d. –49 + 3x + 2 = 6x – 13 – 4x
e. d + 12 3d = 5d 6f. 3m + 6 – 2m = –22
Practice
1. If 4 is subtracted from twice a number, the result is 30. Find the number.
a. Define a variable for the unknown value. Let _____ represent ______
b. Write and solve the equation.
c. Answer the question with the correct units.
2. A cell phone company charges a monthly rate of $12.95 plus $0.25 per minute. Your bill is $21.20. How
many minutes did you use?
a. Define a variable for the unknown value. Let _____ represent ______
b. Write and solve the equation.
c. Answer the question with the correct units.
3. The length of a rectangular map is 15 inches and the perimeter is 50 inches. What is the width?
a. Define a variable for the unknown value. Let _____ represent ______
b. Write and solve the equation.
c. Answer the question with the correct units.
Solve each equation.
4.–12 + 5k = 15 – 4k5.4t + 9 = –8t – 136.22p + 11 = 4p – 7
7.17 – 9y = –3 + 16y8.15m + 22 = –7m + 189.3x + 7 = 14 + 3x
Solve each equation. First, simplify each side by Combining Like Terms.
10. 20 + g +g = 1411. 7 + 4x – 9 = –612. –12 = –5 – 6n + 11
13. t + 10 – 4t = –1114. 8 = 8p + 13 – 3p15. 4y – 16 + 8y = –4
16. 4 – 6h – 8h = 6017. –32 = –7n – 12 + 3n18.7 = 5x + 3x – 6 + 5