Solve Two-Step Linear Equations - 7th Grade Math

1. What is the value of $x$ in $3x+5=20$?

   $x=5$. Subtract $5$, then divide by $3$: $(20-5)÷3=5$.

2. What is the second inverse operation to isolate $x$ in an equation of the form $px+q=r$ after subtracting $q$?

   Divide both sides by $p$. This reverses the multiplication by $p$ to solve for $x$.

3. What is the value of $x$ in $0.4x+1.2=3.6$?

   $x=6$. Subtract $1.2$, divide by $0.4$: $(3.6-1.2)÷0.4=6$.

4. What is the solution for $-3(x+4)=6$?

   $x=-6$. Divide by -3, then subtract 4: $6÷(-3)-4=-6$.

5. What is the value of $x$ in $-2x+7=1$?

   $x=3$. Subtract $7$, divide by $-2$: $(1-7)÷(-2)=3$.

6. What is the first inverse operation to isolate $x$ in an equation of the form $px+q=r$?

   Subtract $q$ from both sides. This isolates the $px$ term on one side of the equation.

7. What is $x$ if a gym charges $10 plus $3 per visit and the total is $25?

   $x=5$. Solve $3x+10=25$: subtract 10, divide by 3.

8. What is $x$ if $-2(x+5)=14$?

   $x=-12$. Divide by -2: $x+5=-7$, then subtract 5.

9. What is the solution for $\frac{3}{4}(x+8)=12$?

   $x=8$. Divide by $\frac{3}{4}$, then subtract 8: $12÷\frac{3}{4}-8=8$.

10. What is the number if $\frac{3}{5}$ of a number, then add 2, gives 11?

    $x=15$. Set up $\frac{3}{5}x+2=11$, solve: $x=15$.

11. What is $x$ if $\frac{2}{3}(x-9)=-4$?

    $x=3$. Divide by $\frac{2}{3}$: $x-9=-6$, then add 9.

12. What equation matches: "A gym charges a $10 fee plus $3 per visit; total is $25. What is $x$?"

    $3x+10=25$. Fixed fee plus cost per visit equals total.

13. What is the first inverse operation to isolate $x$ in an equation of the form $px+q=r$?

    Subtract $q$ from both sides. This reverses the addition of $q$ to begin isolating $x$.

14. What is the solution for $\frac{1}{2}x+3=7$?

    $x=8$. Subtract 3, then multiply by 2: $(7-3)×2=8$.

15. What is the first step to isolate $x$ in an equation of the form $p(x+q)=r$?

    Divide both sides by $p$. This removes the coefficient $p$ from the parentheses.

16. What is $x$ if $4x-7=21$?

    $x=7$. Add 7: $4x=28$, then divide by 4.

17. What is the solution for $5(x-2)=15$?

    $x=5$. Divide by 5, then add 2: $15÷5+2=5$.

18. What equation matches: "You buy $x$ notebooks at $2 each and use a $5 coupon; you pay $13."

    $2x-5=13$. Total cost minus coupon discount equals amount paid.

19. What is $x$ if $\frac{1}{2}x+3=7$?

    $x=8$. Subtract 3: $\frac{1}{2}x=4$, then multiply by 2.

20. What is $x$ if $-3x+5=-10$?

    $x=5$. Subtract 5: $-3x=-15$, then divide by -3.

21. What does the phrase "$\frac{1}{2}$ of a number" translate to, using variable $x$?

    $\frac{1}{2}x$. "Of" means multiply in fraction contexts.

22. Identify the equation that matches: "$3$ more than twice a number is $17$."

    $2x+3=17$. "Twice a number" is $2x$, "3 more" adds 3.

23. What is the second step to isolate $x$ in an equation of the form $p(x+q)=r$ after dividing by $p$?

    Subtract $q$ from both sides. This isolates $x$ after the parentheses are removed.

24. What is the arithmetic meaning of $px+q=r$ in a word problem?

    A number times $p$, then add $q$, equals $r$. Multiply unknown by $p$, add $q$ to get $r$.

25. What is $x$ if you buy $x$ notebooks at $2 each, use a $5 coupon, and pay $13?

    $x=9$. Solve $2x-5=13$: add 5, divide by 2.

26. What is the value of $x$ in $\frac{3}{4}(x+8)=6$?

    $x=0$. Divide by $\frac{3}{4}$, subtract $8$: $6÷\frac{3}{4}-8=0$.

27. What does the phrase "$q$ less than a number" translate to in terms of $x$?

    $x-q$. "Less than" means subtract from the number.

28. What is the arithmetic meaning of $p(x+q)=r$ in a word problem?

    Add $q$ to a number, then multiply by $p$ to get $r$. First add $q$ to unknown, then multiply result by $p$.

29. Identify the equation that matches: "Five times the sum of a number and $4$ is $35$."

    $5(x+4)=35$. "Sum of a number and 4" is $(x+4)$, times 5.

30. What is the number if "Subtract $4$, then multiply by $3$, to get $18$"?

    $x=10$. Set up $3(x-4)=18$, solve: $x=10$.

31. What is $x$ if $6(x-2)=24$?

    $x=6$. Divide by 6: $x-2=4$, then add 2.

32. What is the value of $x$ in $-3(x+2)=15$?

    $x=-7$. Divide by $-3$, subtract $2$: $15÷(-3)-2=-7$.

33. What is $x$ if $0.2x+1=3$?

    $x=10$. Subtract 1: $0.2x=2$, then divide by 0.2.

34. What is the value of $x$ in $1.5(x-4)=9$?

    $x=10$. Divide by $1.5$, add $4$: $9÷1.5+4=10$.

35. What is the equation form for "$p$ times the sum of a number and $q$ is $r$"?

    $p(x+q)=r$. "Times the sum" means multiply the entire addition.

36. Identify the equation form that matches: "$q$ more than $p$ times a number is $r$."

    $px+q=r$. "More than" means addition after multiplication.

37. What is the equation form for "$q$ more than $p$ times a number is $r$"?

    $px+q=r$. "More than" means addition after multiplication.

38. What does the phrase "the quotient of a number and $p$" translate to in terms of $x$?

    $\frac{x}{p}$. "Quotient" means division result.

39. What does the phrase "a number increased by $q$, then multiplied by $p$" translate to?

    $p(x+q)$. "Increased by" means add; "then" shows order of operations.

40. What does the phrase "$q$ less than $p$ times a number" translate to, using variable $x$?

    $px-q$. Multiply first, then subtract $q$ from the result.

41. What does the phrase "$q$ less than $p$ times a number" translate to in terms of $x$?

    $px-q$. "Less than" means subtract from the product.

42. What is the distributive property for expanding $p(x+q)$?

    $p(x+q)=px+pq$. Multiply $p$ by each term inside the parentheses.

43. Identify the equation form that matches: "$p$ times the quantity a number plus $q$ is $r$."

    $p(x+q)=r$. Parentheses show addition happens before multiplication.

44. What is the solution for $2(x-5)+3=9$?

    $x=8$. Simplify to $2x-10+3=9$, then solve $2x-7=9$.

45. What is the solution for $3x+5=20$?

    $x=5$. Subtract 5, then divide by 3: $(20-5)÷3=5$.

46. What is $x$ if $-\frac{3}{4}(x+8)=6$?

    $x=-16$. Divide by $-\frac{3}{4}$: $x+8=-8$, then subtract 8.

47. What is the solution for $0.2x-1=3$?

    $x=20$. Add 1, then divide by 0.2: $(3+1)÷0.2=20$.

48. What is the distributive property rewrite of $p(x+q)$?

    $p(x+q)=px+pq$. Multiply $p$ by each term inside the parentheses.

49. Which form matches: "A gym charges a $12$ fee plus $5$ dollars per class for $c$ classes"?

    $5c+12=r$. Fixed fee $12$ plus variable cost $5c$ equals total $r$.

50. What does the phrase "$q$ less than a number" translate to in algebra, using variable $x$?

    $x-q$. "Less than" means subtract from the number.

51. What is the equation for: "A $12 fee plus $3 per hour totals $30"? Use $h$ for hours.

    $3h+12=30$. Fixed fee plus hourly rate equals total cost.

52. What is the solution for $x$ in $p(x+q)=r$ written as a formula?

    $x=\frac{r}{p}-q$. Divide by $p$ first, then subtract $q$ to isolate $x$.

53. What is the equation for: "$5$ times the sum of a number and $2$ equals $35$"? Use $x$.

    $5(x+2)=35$. "Sum" requires parentheses; "times" indicates multiplication.

54. What is the first inverse operation to isolate $x$ in an equation of the form $p(x+q)=r$?

    Divide both sides by $p$. This removes the parentheses and isolates the $(x+q)$ term.

55. What is the solution for $x$ in $px+q=r$ written as a formula?

    $x=\frac{r-q}{p}$. Subtract $q$, then divide by $p$ to isolate $x$.

56. What is the value of $x$ in $4(x-3)=20$?

    $x=8$. Divide by $4$, add $3$: $20÷4+3=8$.

57. What is the value of $x$ in $\frac{1}{2}x-3=5$?

    $x=16$. Add $3$, multiply by $2$: $(5+3)×2=16$.

58. What is the solution for $-4x+7=-9$?

    $x=4$. Subtract 7, then divide by -4: $(-9-7)÷(-4)=4$.

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