Problem Set: Multi-Step Linear Equations

PROBLEM SET

In the following exercises, solve the linear equation using the general strategy.

1. $4\left(y+7\right)=64$

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2. $9=3\left(x - 3\right)$

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3. $14\left(y - 6\right)=-42$

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4. $-7\left(3n+4\right)=14$

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5. $8\left(3+3\text{p}\right)=0$

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6. $\Large\frac{3}{5}\normalsize\left(10x - 5\right)=27$

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7. $4\left(2.5v - 0.6\right)=7.6$

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8. $0.5\left(16m+34\right)=-15$

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9. $-\left(t - 8\right)=17$

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10. $8\left(6b - 7\right)+23=63$

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11. $13+2\left(m - 4\right)=17$

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12. $-9+6\left(5-k\right)=12$

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13. $18-\left(9r+7\right)=-16$

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14. $18 - 2\left(y - 3\right)=32$

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15. $3\left(4n - 1\right)-2=8n+3$

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16. $5\left(x - 4\right)-4x=14$

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17. $5+6\left(3s - 5\right)=-3+2\left(8s - 1\right)$

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18. $4\left(x - 1\right)-8=6\left(3x - 2\right)-7$

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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 $150=2\left(w+15\right)+2w$ .

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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 $0.05n+0.10\left(2n - 1\right)=1.90$ .

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In the following exercises, solve the equation by clearing the fractions.

19. $\Large\frac{1}{4}\normalsize x-\Large\frac{1}{2}\normalsize =-\Large\frac{3}{4}$

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x = - 1

$x = −1$

20. $\Large\frac{5}{6}\normalsize y-\Large\frac{2}{3}\normalsize =-\Large\frac{3}{2}$

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y = - 1

$y = −1$

21. $\Large\frac{1}{2}\normalsize a+\Large\frac{3}{8}\normalsize =\Large\frac{3}{4}$

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a = \frac{3}{4}

$a=\Large\frac{3}{4}$

22. $2=\Large\frac{1}{3}\normalsize x-\Large\frac{1}{2}\normalsize x+\Large\frac{2}{3}\normalsize x$

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x = 4

$x = 4$

23. $\Large\frac{1}{4}\normalsize m-\Large\frac{4}{5}\normalsize m+\Large\frac{1}{2}\normalsize m=-1$

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m = 20

$m = 20$

24. $x+\Large\frac{1}{2}\normalsize =\Large\frac{2}{3}\normalsize x-\Large\frac{1}{2}$

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x = - 3

$x = −3$

25. $\Large\frac{1}{3}\normalsize w+\Large\frac{5}{4}\normalsize =w-\Large\frac{1}{4}$

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w = \frac{9}{4}

$w=\Large\frac{9}{4}$

26. $\Large\frac{1}{2}\normalsize x-\Large\frac{1}{4}\normalsize =\Large\frac{1}{12}\normalsize x+\Large\frac{1}{6}$

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x = 1

$x = 1$

27. $\Large\frac{1}{3}\normalsize b+\Large\frac{1}{5}\normalsize =\Large\frac{2}{5}\normalsize b-\Large\frac{3}{5}$

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b = 12

$b = 12$

28. $1=\Large\frac{1}{6}\normalsize\left(12x - 6\right)$

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x = 1

$x = 1$

29. $\Large\frac{1}{2}\normalsize\left(x+4\right)=\Large\frac{3}{4}$

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x = - \frac{5}{2}

$x=-\Large\frac{5}{2}$

In the following exercises, solve the equation by clearing the decimals.

30. $0.9x - 1.25=0.75x+1.75$

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x = 20

$x = 20$

31. $0.10d+0.25\left(d+5\right)=4.05$

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d = 8

$d = 8$

32. $0.05\left(q - 5\right)+0.25q=3.05$

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q = 11

$q = 11$

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 $0.10d+0.01\left(d+2\right)=2$ for $d$ , the number of dimes.

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d = 18

$d = 18$

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Module 2: Linear and Quadratic Equations

PROBLEM SET

everyday math

Making a fence

Everyday math

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