ISEE Middle Level Mathematics Achievement Flashcards: Solving For An Unknown

What this deck covers

This deck focuses on Solving For An Unknown, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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

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

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

Answer: 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.

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

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

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

Answer: 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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