PROBLEM SET
In the following exercises, solve the linear equation using the general strategy.
1. 4(y+7)=64
2. 9=3(x−3)
3. 14(y−6)=−42
4. −7(3n+4)=14
5. 8(3+3p)=0
6. 35(10x−5)=27
7. 4(2.5v−0.6)=7.6
8. 0.5(16m+34)=−15
9. −(t−8)=17
10. 8(6b−7)+23=63
11. 13+2(m−4)=17
12. −9+6(5−k)=12
13. 18−(9r+7)=−16
14. 18−2(y−3)=32
15. 3(4n−1)−2=8n+3
16. 5(x−4)−4x=14
17. 5+6(3s−5)=−3+2(8s−1)
18. 4(x−1)−8=6(3x−2)−7
everyday math
Making a fence
Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is 150 feet. The length is 15 feet more than the width. Find the width, w, by solving the equation 150=2(w+15)+2w.
Coins Rhonda has $1.90 in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, n, by solving the equation 0.05n+0.10(2n−1)=1.90.
In the following exercises, solve the equation by clearing the fractions.
19. 14x−12=−34
20. 56y−23=−32
21. 12a+38=34
22. 2=13x−12x+23x
23. 14m−45m+12m=−1
24. x+12=23x−12
25. 13w+54=w−14
26. 12x−14=112x+16
27. 13b+15=25b−35
28. 1=16(12x−6)
29. 12(x+4)=34
In the following exercises, solve the equation by clearing the decimals.
30. 0.9x−1.25=0.75x+1.75
31. 0.10d+0.25(d+5)=4.05
32. 0.05(q−5)+0.25q=3.05
Everyday math
Coins Taylor has $2.00 in dimes and pennies. The number of pennies is 2 more than the number of dimes. Solve the equation 0.10d+0.01(d+2)=2 for d, the number of dimes.
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