2 Mid-Chapter Quiz

Do you know HOW?

Solve each equation. Check your answer.

1. 38 = 2a + 54
2. t + 18.1 = 23.9
3. 18.9 = 2.1x
4. 1 2 ( b − 3 ) = 5 2 1 half . open , b minus 3 , close . equals , 5 halves

Solve each equation. Justify your steps.

5. 9 − 3 r = 14 9 minus 3 r equals 14
6. 3 = 1 2 b + 11 3 equals , 1 half , b plus 11

Solve each equation. If the equation is an identity, write identity. If it has no solution, write no solution.

7. 8 ( h − 1 ) = 6 h + 4 + 2 h 8 open h minus 1 close equals 6 h plus 4 plus 2 h
8. 1 7 ( 14 − 7 p ) − 2 = − 2 ( 1 2 p + 3 ) + 6 1 seventh . open . 14 minus 7 p . close . minus 2 equals negative 2 . open . 1 half , p plus 3 . close . plus 6
9. c + 3 5 = 15 fraction c plus 3 , over 5 end fraction . equals 15
10. 2 3 ( x − 4 ) = 1 3 ( 2 x − 6 ) 2 thirds . open , x minus 4 , close . equals , 1 third . open , 2 x minus 6 , close
11. 1.7m = 10.2
12. 2 + 1 3 t = 1 + 1 4 t 2 plus , 1 third , t equals 1 plus , 1 fourth , t
13. Geometry The formula for the area of a triangle is A = 1 2 b h . eh equals , 1 half , b h .  Solve the formula for h. A triangle has a base of 7 cm and an area of 28 cm 2 . 28 , cm squared , .  What is its height?
14. Menus A new pizza shop is going to print new menus. Each menu costs $.50 to produce. The owners have a total budget of $2500 for the new menus. How many menus can the pizza shop print?
15. Guitars You paid $600 for a new guitar. Your guitar cost $40 more than twice the cost of your friend's guitar. How much did your friend's guitar cost?

Define a variable and write an equation to model each situation. Then solve.

16. Concerts Concert tickets cost $25 each. A college student ordered some tickets online. There was a service charge of $3 per ticket. The total came to $252. How many tickets did the student order?
17. Gyms Membership for the Alpine rock-climbing gym costs $25 per month plus a $125 sign-up fee. Membership for Rocco's rock-climbing gym costs $30 per month plus a $50 sign-up fee.
    1. After how many months will the memberships cost the same?
    2. If you only wanted a one-year membership, which gym would you join?

Do you UNDERSTAND?

18. Vocabulary Complete: You can use subtraction to undo addition. Subtraction is called the _ ? modified under bar with question mark above  of addition.
19. Reasoning The equation 5 x = 2 x + 3 x 5 over x , equals , 2 over x , plus , 3 over x  is true for all values of x where x ≠ 0 . x not equal to 0 .  Is the equation an identity?
20. Writing Would you solve the equation 10 = 4 ( y − 1 ) 10 equals 4 open y minus 1 close  by using the Distributive Property or by dividing each side by 4? Explain.
21. Reasoning In the process of solving an equation, a student noticed that the variable was eliminated. The student concluded that the equation must be an identity. Is the student correct? Explain.
22. Reasoning You are solving the equation 0.02 x − 0.004 = 0.028 . 0.02 , x minus , 0.004 , equals , 0.028 , .  Your first step is to multiply both sides by 1000 to clear the decimals. Your classmate starts by dividing both sides by 0.02. Is there any disadvantage to your classmate's method? Explain.

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