Linear Equations in One Variable Practice

Sample questions

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1. Sample 1difficulty 2/5

   If $\frac{x}{4} + 2 = 7$, what is the value of $x$?

   • A

     $\frac{9}{4}$

   • B

     9

   • C

     20

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   • D

     5

   Why

   Subtract 2: $\frac{x}{4} = 5$. Multiply by 4: $x = 20$.

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2. Sample 2difficulty 2/5

   What are the solutions to $|x - 4| = 7$?

   • A

     $x = 11$ only

   • B

     $x = -3$ or $x = 11$

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   • C

     $x = 3$ or $x = -11$

   • D

     $x = -3$ only

   Why

   $x - 4 = 7$ gives $x = 11$; $x - 4 = -7$ gives $x = -3$.

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3. Sample 3difficulty 2/5

   A bag contains nickels and dimes worth \2.50$ total. There are 30 coins in all. How many dimes are in the bag?

   • A

     20

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   • B

     25

   • C

     10

   • D

     15

   Why

   Let $n$ = nickels, $d$ = dimes. $n + d = 30$, $0.05n + 0.10d = 2.50$. Substitute $n = 30 - d$: $0.05(30-d) + 0.10d = 2.50$ → $1.5 + 0.05d = 2.50$ → $d = 20$.

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4. Sample 4difficulty 2/5

   If $|x - 4| = 3$, which of the following could be a value of $x$?

   • A

     $-1$

   • B

     12

   • C

     $-7$

   • D

     1

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   Why

   $x - 4 = 3$ gives $x = 7$, or $x - 4 = -3$ gives $x = 1$. Among the choices, 1 works.

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5. Sample 5difficulty 2/5

   If $3x - 7 = 14$, what is the value of $x$?

   • A

     5

   • B

     7

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   • C

     $\frac{7}{3}$

   • D

     21

   Why

   Add 7 to both sides: $3x = 21$. Divide by 3: $x = 7$.

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