8th Grade Math Flashcards: Solve Linear Equations With Rationals

What this deck covers

This deck focuses on Solve Linear Equations With Rationals, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

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 $\frac{2}{5}x = 6$?

Answer: $x = 15$. Multiply both sides by $\frac{5}{2}$: $x = 6 \cdot \frac{5}{2} = 15$.

Flashcard 2: What is the solution to $\frac{1}{3}x - 2 = 4$?

Answer: $x = 18$. Add 2, then multiply by 3: $(4+2) \cdot 3 = 18$.

Flashcard 3: What is the solution to $\frac{3}{4}x + \frac{1}{2} = 2$?

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

Flashcard 4: What is the solution to $\frac{2}{3}(x - 6) = 4$?

Answer: $x = 12$. Multiply by $\frac{3}{2}$, then add 6: $4 \cdot \frac{3}{2} + 6 = 12$.

Flashcard 5: What is the solution to $\frac{1}{2}(4x + 6) = 9$?

Answer: $x = 3$. Distribute, then solve: $2x + 3 = 9$, so $2x = 6$, $x = 3$.

Flashcard 6: What is the solution to $\frac{5}{6}x - \frac{1}{3} = \frac{1}{2}$?

Answer: $x = 1$. Add $\frac{1}{3}$ to get $\frac{5}{6}x = \frac{5}{6}$, then $x = 1$.

Flashcard 7: What is the solution to $\frac{1}{4}x + \frac{1}{2}x = 6$?

Answer: $x = 8$. Combine like terms: $\frac{3}{4}x = 6$, then $x = 8$.

Flashcard 8: What is the solution to $2(x - \frac{3}{2}) = 5$?

Answer: $x = 4$. Distribute 2, then solve: $2x - 3 = 5$, so $x = 4$.

Flashcard 9: What is the solution to $\frac{3}{5}x + 2 = \frac{1}{5}x + 6$?

Answer: $x = 10$. Subtract $\frac{1}{5}x$ and 2: $\frac{2}{5}x = 4$, so $x = 10$.

Flashcard 10: What is the solution to $x + \frac{3}{8} = \frac{7}{8}$?

Answer: $x = \frac{1}{2}$. Subtract $\frac{3}{8}$ from both sides: $x = \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2}$.

Flashcard 11: What is the LCD of $\frac{1}{6}$, $\frac{1}{4}$, and $\frac{1}{3}$?

Answer: $12$. Find the smallest number divisible by 6, 4, and 3.

Flashcard 12: What is the solution to $\frac{1}{2}x - \frac{3}{4} = \frac{1}{4}x + \frac{1}{2}$?

Answer: $x = 5$. Subtract $\frac{1}{4}x$, add $\frac{3}{4}$: $\frac{1}{4}x = \frac{5}{4}$, so $x = 5$.

Flashcard 13: What is the solution to $\frac{x}{3} + \frac{x}{6} = 5$?

Answer: $x = 10$. Combine fractions: $\frac{2x}{6} + \frac{x}{6} = \frac{3x}{6} = \frac{x}{2} = 5$.

Flashcard 14: What is the solution to $\frac{2}{3}x + \frac{1}{2} = \frac{1}{6}x + \frac{5}{2}$?

Answer: $x = 4$. Subtract $\frac{1}{6}x$ and $\frac{1}{2}$: $\frac{1}{2}x = 2$, so $x = 4$.

Flashcard 15: What is the inverse operation for subtracting $\frac{7}{3}$ from $x$ in $x - \frac{7}{3}$?

Answer: Add $\frac{7}{3}$. Addition undoes subtraction to isolate the variable.

Flashcard 16: What is the result after combining like terms: $\frac{3}{4}x - \frac{1}{2}x$?

Answer: $\frac{1}{4}x$. Convert to common denominator: $\frac{3}{4}x - \frac{2}{4}x = \frac{1}{4}x$.

Flashcard 17: What does it mean to collect like terms in $2x + 5 - x$?

Answer: Combine terms with the same variable and exponent. Add or subtract coefficients of matching variables.

Flashcard 18: Identify the simplified expression: $\frac{1}{2}(6x - 8)$.

Answer: $3x - 4$. Distribute $\frac{1}{2}$ to both terms: $\frac{6x}{2} - \frac{8}{2}$.

Flashcard 19: What property lets you rewrite $3(x - 4)$ as $3x - 12$?

Answer: Distributive property. Multiply each term inside parentheses by the outside factor.

Flashcard 20: What is $x$ in the equation x+rac{2}{3}=rac{5}{3}?

Answer: $x=1$. Subtract rac{2}{3} from both sides.

Flashcard 21: What is $x$ in the equation $3(x-4)=15$?

Answer: $x=9$. Distribute, add 12, then divide by 3.

Flashcard 22: What is $x$ in the equation $3x-2(x+4)=1$?

Answer: $x=9$. Distribute, combine like terms, then solve.

Flashcard 23: What is $x$ in the equation rac{2}{5}x-rac{1}{5}=1?

Answer: $x=3$. Add rac{1}{5}, then multiply by rac{5}{2}.

Flashcard 24: What is $x$ in the equation rac{2}{3}(x-3)+1=3?

Answer: $x=6$. Distribute rac{2}{3}, then isolate $x$.

Flashcard 25: What is the first step to solve $3(x-4)=15$?

Answer: Distribute: $3x-12=15$. Apply $3(x-4)=3x-12$ to expand the left side.

Flashcard 26: What is $x$ in the equation x-rac{5}{6}=rac{1}{6}?

Answer: $x=1$. Add rac{5}{6} to both sides to get x=rac{6}{6}=1.

Flashcard 27: What property lets you multiply both sides of $a=b$ by the same nonzero number $c$?

Answer: Multiplication Property of Equality. If $a=b$, then $ac=bc$ for any nonzero $c$.

Flashcard 28: What does it mean to solve a linear equation in one variable?

Answer: Find the value of $x$ that makes the equation true. The solution is the value that satisfies the equation.

Flashcard 29: What is $x$ in the equation rac{1}{2}(x+6)=5?

Answer: $x=4$. Multiply both sides by 2, then subtract 6.

Flashcard 30: What is $x$ in the equation $5-2(x+1)=1$?

Answer: $x=1$. Distribute $-2$, then solve for $x$.