Linear Inequalities - SAT Math

1. What is the solution to $4x + 8 < 16$?

   $x < 2$. Subtract 8, divide by 4 to solve inequality.

2. What is the solution to $3(x - 2) < 6$?

   $x < 4$. Distribute 3, add 6 to both sides, then divide by 3.

3. What inequality represents a number $x$ is less than $10$?

   $x < 10$. Standard notation for values below 10.

4. What is the solution set for $5x + 2 \neq 12$?

   $x \neq 2$. Subtract 2, divide by 5 to find excluded value.

5. Solve $-3x + 7 \neq 1$ for $x$.

   $x \neq 2$. Subtract 7, divide by -3 to get $x = 2$.

6. Solve $0 < 2x + 4$ for $x$.

   $x > -2$. Subtract 4, divide by 2 to solve inequality.

7. Solve the inequality: $5x - 4 \text{ } \text{≤} \text{ } 11$.

   $x \text{ } \text{≤} \text{ } 3$. Add 4 to both sides, then divide by 5.

8. What inequality symbol represents 'greater than or equal to'?

   $\geq$. Combines greater than and equal to in one symbol.

9. Solve for $x$: $3(x - 2) \geq 9$.

   $x \geq 5$. Distribute 3, add 6 to both sides, then divide by 3.

10. Find the value of $x$ in $5x - 3 < 2x + 6$.

    $x < 3$. Move $2x$ left and $-3$ right, then divide by 3.

11. Solve $-5x \neq 10$ for $x$.

    $x \neq -2$. Divide both sides by -5 to isolate $x$.

12. Identify the inequality symbol for 'greater than'.

    $>$. Symbol for strict inequality without equality.

13. What is the solution to the inequality $2x + 3 > 7$?

    $x > 2$. Subtract 3 from both sides, then divide by 2.

14. Identify the solution set for $2x + 5 > 9$.

    The solution set is $x > 2$. Subtract 5 from both sides, then divide by 2.

15. Determine if $x = -1$ satisfies $2x + 3 > 0$.

    No, $x = -1$ does not satisfy $2x + 3 > 0$. Substituting gives $2(-1) + 3 = 1 > 0$ is false.

16. What does the inequality $x \text{ } \text{≤} \text{ } 0$ indicate about $x$?

    $x$ is less than or equal to zero. The variable can be zero or any negative value.

17. What is the solution to $4 - x > 8$?

    $x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.

18. Solve for $x$: $3(x - 2) \geq 9$.

    $x \geq 5$. Distribute 3, add 6 to both sides, then divide by 3.

19. Solve $8 - x \neq 5$ for $x$.

    $x \neq 3$. Solve $x = 3$ from the equation $8 - x = 5$.

20. Solve the inequality $-2x + 9 < 3$ for $x$.

    $x > 3$. Subtract 9, divide by -2, flip inequality sign.

21. How do you graph $x > 3$ on a number line?

    Open circle at 3, arrow to the right. Open circle shows 3 is not included.

22. What is the inequality for 'y is less than 8'?

    $y < 8$. 'Less than' means strictly smaller than 8.

23. Which symbol represents 'greater than or equal to'?

    $\geq$. Standard mathematical symbol for greater than or equal to.

24. Solve $-4x + 5 eq -11$ for $x$.

    $x eq 4$. Add 11, divide by -4 to get $x = 4$.

25. What is the inequality for 'x is at least 5'?

    $x \geq 5$. 'At least' means greater than or equal to.

26. What does the inequality $x < 0$ represent?

    Negative numbers. All values to the left of zero on number line.

27. Solve $x - 5 \geq 0$ for $x$.

    $x \geq 5$. Add 5 to both sides to isolate $x$.

28. How do you graph $x \leq -2$ on a number line?

    Closed circle at -2, arrow to the left. Closed circle includes -2 in the solution set.

29. What is the solution to $x/3 \neq 2$?

    $x \neq 6$. Multiply both sides by 3 to isolate $x$.

30. Solve $2x + 3 \leq 7$ for $x$.

    $x \leq 2$. Subtract 3, divide by 2 to solve inequality.

31. Solve $4 - 2x \neq 0$ for $x$.

    $x \neq 2$. Solve $2x = 4$ to find the excluded value.

32. What is the inequality for 'x is more than 10'?

    $x > 10$. 'More than' means strictly greater than.

33. State the rule for reversing an inequality sign.

    Multiply or divide both sides by a negative number. This operation changes the direction of the inequality.

34. Solve $7x - 3 \neq 25$ for $x$.

    $x \neq 4$. Add 3, divide by 7 to find excluded value.

35. Solve $3x + 7 \leq 16$ for $x$.

    $x \leq 3$. Subtract 7, divide by 3 to isolate $x$.

36. What is the solution set for $3(x - 4) < 6$?

    $x < 6$. Distribute 3, add 12, then divide by 3.

37. Solve $-3(x + 4) \neq 9$ for $x$.

    $x \neq -7$. Distribute -3, subtract 12, divide by -3.

38. What inequality symbol represents 'less than or equal to'?

    $\leq$. Combines less than and equal to in one symbol.

39. What is the solution to the inequality $-3x \neq 9$?

    $x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.

40. What is the solution to $x + 3 > 10$?

    $x > 7$. Subtract 3 from both sides to isolate $x$.

41. What is the graphical representation of $y \neq 4$?

    A horizontal line at $y = 4$ with a dashed line. Uses dashed line since $\neq$ excludes the boundary value.

42. What is the inequality representation of 'p is at most 4'?

    $p \leq 4$. 'At most' means less than or equal to.

43. Solve the inequality: $-2y + 5 \text{ } \text{≥} \text{ } 11$.

    $y \text{ } \text{≤} \text{ } -3$. Subtract 5, divide by $-2$, and flip the inequality sign.

44. Solve $6(x - 2) > 12$ for $x$.

    $x > 4$. Distribute 6, add 12, then divide by 6.

45. Solve $5 - 2x \neq 13$ for $x$.

    $x \neq -4$. Subtract 5, divide by -2 to get $x = -4$.

46. State the inequality that represents $x$ is at most 7.

    $x \leq 7$. 'At most' means less than or equal to.

47. How would you express $4$ is less than or equal to $x$?

    $4 \leq x$. Reverses the typical order to show 4 as the lesser value.

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