Multi-Step Equations - SSAT Middle Level Quantitative

1. What is $x$ in $\frac{x}{4}-\frac{1}{2}=\frac{3}{2}$?

   $x=8$. Add $\frac{1}{2}$ to both sides to get $\frac{x}{4}=2$, then multiply by 4.

2. What is $x$ in $\frac{x}{3}+2=6$?

   $x=12$. Subtract 2 from both sides to get $\frac{x}{3}=4$, then multiply by 3.

3. What is $x$ in $\frac{1}{3}(x+6)=5$?

   $x=9$. Multiply both sides by 3 to get $x+6=15$, then subtract 6.

4. What is $x$ in $2(x+4)=18$?

   $x=5$. Divide both sides by 2 to get $x+4=9$, then subtract 4 using properties of equality.

5. What is $x$ in $\frac{x-5}{2}+\frac{x+1}{2}=10$?

   $x=12$. Combine fractions to get $\frac{2x-4}{2}=10$, simplify to $x-2=10$, then add 2.

6. What is $x$ in $\frac{2x-1}{3}=5$?

   $x=8$. Multiply both sides by 3 to get $2x-1=15$, then add 1 and divide by 2.

7. What is the LCD used to clear denominators in $\frac{x}{6}+\frac{1}{4}=2$?

   $12$. The least common denominator of 6 and 4 is 12, allowing multiplication through the equation to eliminate fractions.

8. What is $x$ in $2x+7=5x-8$?

   $x=5$. Add 8 to both sides and subtract $2x$ to get $15=3x$, then divide by 3.

9. What is $x$ in $2x-3=2x+5$?

   No solution. Subtracting $2x$ from both sides yields $-3=5$, a false statement indicating no value satisfies the equation.

10. What is $x$ in $4(x-2)+3=19$?

    $x=6$. Distribute 4 to get $4x-8+3=19$, combine constants, add 5, then divide by 4.

11. What is $x$ in $9-2x=1$?

    $x=4$. Subtract 9 from both sides to get $-2x=-8$, then divide by -2.

12. What property justifies adding the same number to both sides of $x-7=12$?

    Addition Property of Equality. This property states that adding the same value to both sides of an equation preserves the equality while isolating the variable.

13. What is the first step to solve $3x+5=20$?

    Subtract $5$ from both sides. Subtracting 5 from both sides isolates the term with the variable using the subtraction property of equality.

14. What property justifies multiplying both sides of $\frac{x}{5}=9$ by $5$?

    Multiplication Property of Equality. This property allows multiplying both sides by the same nonzero number to maintain equality and solve for the variable.

15. What is $x$ in $3(x+2)-4=11$?

    $x=3$. Distribute 3 to get $3x+6-4=11$, combine constants, subtract 2, then divide by 3.

16. What is $x$ in $3x+5=20$?

    $x=5$. Subtract 5 from both sides to get $3x=15$, then divide by 3 using properties of equality.

17. What is $x$ in $\frac{3}{4}x+2=8$?

    $x=8$. Subtract 2 from both sides to get $\frac{3}{4}x=6$, then multiply by $\frac{4}{3}$.

18. What is $x$ in $7+4x=3x+19$?

    $x=12$. Subtract $3x$ from both sides and subtract 7 to isolate the variable using properties of equality.

19. What is $x$ in $5x-3=2x+12$?

    $x=5$. Subtract $2x$ from both sides and add 3 to isolate the variable term, then divide by 3.

20. What is $x$ in $4(x+1)=4x+4$?

    Infinitely many solutions. Distributing 4 yields $4x+4=4x+4$, an identity true for all real values of $x$.

21. What is $x$ in $3(x-1)=2(x+4)$?

    $x=11$. Distribute to get $3x-3=2x+8$, subtract $2x$, add 3, using properties of equality.

22. What is $x$ in $0.2x-1=3$?

    $x=20$. Add 1 to both sides to get $0.2x=4$, then divide by 0.2 or multiply by 5.

23. What is $x$ in $\frac{x}{6}+\frac{1}{4}=2$?

    $x=\frac{21}{2}$. Multiply through by 12 to get $2x+3=24$, subtract 3, then divide by 2.

24. What is $x$ in $0.5x+3=7$?

    $x=8$. Subtract 3 from both sides to get $0.5x=4$, then divide by 0.5 or multiply by 2.

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