Linear Inequalities in One or Two Variables Practice

Sample questions

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1. Sample 1difficulty 2/5

   Three less than a number is at most $10$. Which inequality represents this?

   • A

     $n - 3 \leq 10$

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   • B

     $3 - n \leq 10$

   • C

     $n - 3 < 10$

   • D

     $n + 3 \leq 10$

   Why

   "Three less than a number" is $n - 3$, and "at most 10" is $\leq 10$.

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2. Sample 2difficulty 2/5

   Which of the following is the solution to $-3x + 6 \geq 0$?

   • A

     $x \leq 2$

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   • B

     $x \geq -2$

   • C

     $x \leq -2$

   • D

     $x \geq 2$

   Why

   Subtract 6: $-3x \geq -6$. Divide by $-3$ (flip sign): $x \leq 2$.

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3. Sample 3difficulty 2/5

   Which inequality is equivalent to $-2x + 3 > 11$?

   • A

     $x < -4$

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   • B

     $x < 4$

   • C

     $x > 4$

   • D

     $x > -4$

   Why

   $-2x > 8$, so $x < -4$ (flip when dividing by a negative).

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4. Sample 4difficulty 2/5

   Which of the following is the solution to $2x + 5 > 11$?

   • A

     $x > 8$

   • B

     $x \geq 3$

   • C

     $x > 3$

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   • D

     $x < 3$

   Why

   Subtract 5: $2x > 6$. Divide by 2: $x > 3$.

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5. Sample 5difficulty 2/5

   What is the solution set of $3x - 5 \le 7$?

   • A

     $x \le 2/3$

   • B

     $x \le 4$

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   • C

     $x \ge 4$

   • D

     $x \le 12/3$

   Why

   $3x \le 12$, so $x \le 4$.

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