Solve One-Step Equations - 6th Grade Math

1. What is $x$ in the equation $x + \frac{3}{4} = 5$?

   $x = \frac{17}{4}$. Subtract $\frac{3}{4}$: $5 - \frac{3}{4} = \frac{20}{4} - \frac{3}{4} = \frac{17}{4}$.

2. What is $x$ in the equation $x + 7 = 19$?

   $x = 12$. Subtract $7$ from both sides: $19 - 7 = 12$.

3. What is $x$ if you split $18$ dollars equally among $6$ people ($6x = 18$)?

   $x = 3$. Divide total dollars by number of people: $18 \div 6 = 3$.

4. What is $x$ if $\frac{2}{3}x = 10$?

   $x = 15$. Multiply both sides by $\frac{3}{2}$: $10 \times \frac{3}{2} = 15$.

5. What is $x$ if $x + 9.4 = 10$?

   $x = 0.6$. Subtract 9.4 from both sides: $10 - 9.4 = 0.6$.

6. What operation isolates $x$ in an equation of the form $x + p = q$?

   Subtract $p$ from both sides. This inverse operation cancels the addition to isolate $x$.

7. What is the solution for $x$ in $px = q$ written in terms of $p$ and $q$ (with $p>0$)?

   $x = \frac{q}{p}$. Dividing both sides by $p$ isolates $x$.

8. What is $x$ if $3$ identical tickets cost $18, so $3x = 18$?

   $x = 6$. Each ticket costs $\$18 ÷ 3 = \$6$.

9. What equation matches: "A number multiplied by $5$ equals $30$"?

   $5x = 30$. "Multiplied by" translates to multiplication.

10. What operation isolates $x$ in $x + p = q$?

    Subtract $p$ from both sides. Subtraction undoes addition to isolate $x$.

11. What is the solution for $x$ in the equation $px = q$ when $p > 0$?

    $x = \frac{q}{p}$. Divide both sides by $p$ to isolate $x$.

12. Identify the value of $x$ that makes $\frac{1}{4}x = 0$ true.

    $x = 0$. Any number times $0$ equals $0$.

13. What equation matches: "A number increased by $9$ is $20$"?

    $x + 9 = 20$. "Increased by" means addition in algebraic form.

14. What is the solution for $x$ in $x + p = q$ written in terms of $p$ and $q$?

    $x = q - p$. Subtracting $p$ from both sides gives the solution.

15. What equation models: "A number increased by $8$ is $20$" using $x$ for the number?

    $x + 8 = 20$. "Increased by" means addition in algebraic expressions.

16. What is the solution for $x$ in the equation $x + p = q$?

    $x = q - p$. Subtract $p$ from both sides to isolate $x$.

17. What is $x$ if a book costs $12 and you have $5 already saved, so $x + 5 = 12$?

    $x = 7$. Need $7 more: $12 - 5 = 7$.

18. What is $x$ if "A number increased by $2.5$ is $10$"?

    $x = 7.5$. Set up $x + 2.5 = 10$, then subtract $2.5$.

19. What is $x$ if $4x = 20$?

    $x = 5$. Divide both sides by 4: $20 ÷ 4 = 5$.

20. Identify the value of $x$ that makes $x + 2.5 = 2.5$ true.

    $x = 0$. Adding $0$ to $2.5$ gives $2.5$.

21. What is $x$ if $x + \frac{3}{4} = 5$?

    $x = \frac{17}{4}$. Subtract $\frac{3}{4}$ from $5$: $\frac{20}{4} - \frac{3}{4} = \frac{17}{4}$.

22. What is $x$ if $8x = 2$?

    $x = \frac{1}{4}$. Divide both sides by $8$: $2 \div 8 = \frac{1}{4}$.

23. What is $x$ in the equation $x + \frac{2}{5} = \frac{9}{5}$?

    $x = \frac{7}{5}$. Subtract $\frac{2}{5}$: $\frac{9}{5} - \frac{2}{5} = \frac{7}{5}$.

24. What equation models: "$\frac{3}{5}$ of a number is $12$" using $x$ for the number?

    $\frac{3}{5}x = 12$. "Of" means multiplication when dealing with fractions.

25. What is the equation for: a number $x$ plus $5$ equals $13$?

    $x + 5 = 13$. Translate words to algebraic form with addition.

26. What is $x$ in the equation $4x = 28$?

    $x = 7$. Divide both sides by $4$: $28 ÷ 4 = 7$.

27. What operation isolates $x$ in $px = q$ when $p \neq 0$?

    Divide both sides by $p$. Division undoes multiplication to isolate $x$.

28. What operation isolates $x$ in an equation of the form $px = q$ (with $p>0$)?

    Divide both sides by $p$. Division is the inverse of multiplication, isolating $x$.

29. What is $x$ in the equation $\frac{2}{3}x = \frac{10}{3}$?

    $x = 5$. Multiply by $\frac{3}{2}$: $\frac{10}{3} × \frac{3}{2} = 5$.

30. What is $x$ if "A number multiplied by $\frac{1}{4}$ equals $3$"?

    $x = 12$. Set up $\frac{1}{4}x = 3$, then multiply by $4$.

31. What is the equation for: $8$ times a number $x$ equals $36$?

    $8x = 36$. Translate words to algebraic form with multiplication.

32. What is $x$ if $4x = 28$?

    $x = 7$. Divide both sides by $4$: $28 \div 4 = 7$.

33. What is $x$ in the equation $\frac{3}{4}x = 9$?

    $x = 12$. Multiply both sides by $\frac{4}{3}$: $9 × \frac{4}{3} = 12$.

34. What is $x$ in the equation $0.5x = 6$?

    $x = 12$. Divide both sides by $0.5$: $6 ÷ 0.5 = 12$.

35. What is $x$ in the equation $x + 0.6 = 2.1$?

    $x = 1.5$. Subtract $0.6$ from both sides: $2.1 - 0.6 = 1.5$.

36. What equation models: "A number plus $\frac{1}{2}$ equals $3$" using $x$ for the number?

    $x + \frac{1}{2} = 3$. "Plus" translates directly to addition in equations.

37. What is $x$ if a $12$ mile trip has $3$ miles left ($x + 3 = 12$)?

    $x = 9$. Miles traveled plus miles left equals total: $12 - 3 = 9$.

38. What is the unknown in $x + p = q$ meant to represent in a word problem?

    The missing quantity (the value to find). The variable represents what we're solving for.

39. What is $x$ if $x + 0.6 = 2.1$?

    $x = 1.5$. Subtract 0.6 from both sides: $2.1 - 0.6 = 1.5$.

40. Identify $x$ in the equation $x + p = q$ when $p = 0$ and $q = 8$.

    $x = 8$. When $p = 0$, the equation becomes $x + 0 = 8$.

41. What is the value of $q$ if $px = q$, $p = 6$, and $x = 2$?

    $q = 12$. Multiply $p$ and $x$: $6 \times 2 = 12$.

42. What equation models: "$6$ times a number is $42$" using $x$ for the number?

    $6x = 42$. "Times" indicates multiplication in algebraic form.

43. What is $x$ if $x + 7 = 19$?

    $x = 12$. Subtract 7 from both sides: $19 - 7 = 12$.

44. What is $x$ if $0.25x = 3$?

    $x = 12$. Divide both sides by 0.25: $3 ÷ 0.25 = 12$.

45. What is $x$ if $0.5x = 6$?

    $x = 12$. Divide both sides by $0.5$: $6 \div 0.5 = 12$.

46. What is the value of $q$ if $x + 3 = q$ and $x = 5$?

    $q = 8$. Substitute $x = 5$ into the equation: $5 + 3 = 8$.

Study these flashcards