Solving for an Unknown - ISEE Middle Level Mathematics Achievement

1. What is the solution to $\frac{3}{4}x = 12$?

   $x = 16$. Multiply both sides by $\frac{4}{3}$ to isolate $x$.

2. What property justifies adding the same number to both sides of an equation?

   Addition Property of Equality. This property maintains the equality of an equation by allowing the addition of the same value to both sides without changing the solution.

3. What is the solution to $3(x - 2) = 15$?

   $x = 7$. Divide both sides by 3, then add 2 to isolate $x$.

4. What is the goal of solving an equation for an unknown variable?

   Isolate the variable to find its value. Solving equations requires performing inverse operations to express the variable alone on one side, revealing its value that satisfies the equation.

5. What is the solution to $6x - 4 = 2x + 12$?

   $x = 4$. Subtract $2x$ from both sides, then add 4 to isolate $x$ and divide by 4.

6. What property justifies multiplying both sides of an equation by the same nonzero number?

   Multiplication Property of Equality. This property preserves equality when both sides are multiplied by the same nonzero number, enabling isolation of variables.

7. What is the solution to $\frac{5}{2}x - 1 = 9$?

   $x = 4$. Add 1 to both sides, then multiply by $\frac{2}{5}$ to isolate $x$.

8. What is the solution to $0.2x + 1 = 3$?

   $x = 10$. Subtract 1 from both sides, then divide by 0.2 to isolate $x$.

9. What is the solution to $0.5x = 8$?

   $x = 16$. Divide both sides by 0.5, or multiply by 2, to isolate $x$.

10. What is the solution to $\frac{2x}{3} = 10$?

    $x = 15$. Multiply both sides by $\frac{3}{2}$ to isolate $x$.

11. What is the solution to $2x + 5 = x + 12$?

    $x = 7$. Subtract $x$ from both sides, then subtract 5 to isolate $x$.

12. What is the solution to $3x + 2 = 20$?

    $x = 6$. Subtract 2 from both sides, then divide by 3 to isolate $x$.

13. What is the solution to $x + 7 = 19$?

    $x = 12$. Subtract 7 from both sides to isolate $x$, using the subtraction property of equality.

14. What is the solution to $\frac{x - 1}{4} = 3$?

    $x = 13$. Multiply both sides by 4, then add 1 to isolate $x$.

15. What is the solution to $7 - 2x = 1$?

    $x = 3$. Subtract 7 from both sides, then divide by -2 to isolate $x$.

16. What is the inverse operation of multiplying by $a$ when solving an equation?

    Dividing by $a$ (for $a \ne 0$). To reverse multiplication and solve for the variable, perform division by $a$ on both sides, provided $a \ne 0$.

17. What is the solution to $\frac{x}{6} = 4$?

    $x = 24$. Multiply both sides by 6 to isolate $x$, applying the multiplication property of equality.

18. What is the solution to $\frac{x}{5} - 3 = 1$?

    $x = 20$. Add 3 to both sides, then multiply by 5 to isolate $x$.

19. What is the solution to $4x - 11 = 9$?

    $x = 5$. Add 11 to both sides, then divide by 4 to isolate $x$.

20. What is the solution to $5x = 45$?

    $x = 9$. Divide both sides by 5 to isolate $x$, using the division property of equality.

21. What is the solution to $x - 9 = -4$?

    $x = 5$. Add 9 to both sides to isolate $x$, applying the addition property of equality.

22. What is the inverse operation of adding $a$ when solving an equation?

    Subtracting $a$. To undo addition and isolate the variable, apply the inverse by subtracting $a$ from both sides of the equation.

23. What is the solution to $2(x + 3) = 14$?

    $x = 4$. Divide both sides by 2, then subtract 3 to isolate $x$.

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