8th Grade Math Flashcards: Classify Solutions To Linear Equations

What this deck covers

This deck focuses on Classify Solutions To Linear Equations, 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: Identify the solution type of $8x=8x-4$.

Answer: No solution. Subtracting $8x$ from both sides gives $0=-4$, which is false.

Flashcard 2: Which result shows exactly one solution: $x=0$, $6=6$, or $2=5$?

Answer: $x=0$. This gives one specific value for $x$ ($x=a$ form).

Flashcard 3: Identify the solution type for $3x+5=3x+2$ after simplifying.

Answer: No solutions. Subtracting $3x$ from both sides gives $5=2$, which is false.

Flashcard 4: What is the solution to $7-2x=1$?

Answer: $x=3$. Subtract $7$, divide by $-2$.

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

Answer: $x=9$. Subtract $2$, multiply by $3$.

Flashcard 6: Identify the solution type for $4(x-2)=4x-8$ after simplifying.

Answer: Infinitely many solutions. Expanding gives $4x-8=4x-8$, which is always true.

Flashcard 7: Identify the solution type for $2x+7=17$ after simplifying.

Answer: $1$ solution. Solving gives $x=5$, one specific value.

Flashcard 8: What does the equation form $a=a$ indicate about the number of solutions?

Answer: Infinitely many solutions. When simplified to $a=a$, the equation is always true for any $x$.

Flashcard 9: Identify the solution type for $3(2x-5)=6x-15$ after simplifying.

Answer: Infinitely many solutions. Expanding gives $6x-15=6x-15$, which is always true.

Flashcard 10: Identify the solution type for $8x=8x+6$ after simplifying.

Answer: No solutions. Subtracting $8x$ gives $0=6$, which is false.

Flashcard 11: Identify the solution type for $9x+1=9x-4$ after simplifying.

Answer: No solutions. Subtracting $9x$ gives $1=-4$, which is false.

Flashcard 12: Identify the solution type for $6x-3=6x-3$ after simplifying.

Answer: Infinitely many solutions. Both sides are identical, so the equation is always true.

Flashcard 13: What does the equation form $x=a$ indicate about the number of solutions?

Answer: $1$ solution. When simplified to $x=a$, the variable equals one specific value.

Flashcard 14: What is the solution to $2(x+4)=18$?

Answer: $x=5$. Expand to get $2x+8=18$, then solve.

Flashcard 15: Identify the solution type for $\frac{x}{2}+1=\frac{x}{2}+1$ after simplifying.

Answer: Infinitely many solutions. Both sides are identical, so the equation is always true.

Flashcard 16: What does the equation form $a=b$ with $a\ne b$ indicate about the number of solutions?

Answer: No solutions. When simplified to $a=b$ where $a≠b$, the equation is never true.

Flashcard 17: Which result shows infinitely many solutions: $x=5$, $7=7$, or $3=9$?

Answer: $7=7$. This is a true statement ($a=a$ form), so any value of $x$ works.

Flashcard 18: Which result shows no solutions: $x=-2$, $4=4$, or $8=1$?

Answer: $8=1$. This is a false statement ($a=b$ form where $a≠b$).

Flashcard 19: Identify the solution type for $\frac{3}{4}x=6$.

Answer: One solution. Multiply both sides by rac{4}{3} to get $x=8$.

Flashcard 20: Which equation has infinitely many solutions: $5x=5x+2$ or $7(x-1)=7x-7$?

Answer: $7(x-1)=7x-7$. The second expands to $7x-7=7x-7$, an identity.

Flashcard 21: Transform $8x-2=8x+1$ to one of the forms $x=a$, $a=a$, or $a=b$.

Answer: $-2=1$ (an $a=b$ form). Subtracting $8x$ from both sides gives this contradiction.

Flashcard 22: Transform $6x+5=6x+5$ to one of the forms $x=a$, $a=a$, or $a=b$.

Answer: $0=0$ (an $a=a$ form). Subtracting $6x+5$ from both sides gives this identity.

Flashcard 23: Find the solution type for $9x-3=6x+12$.

Answer: One solution. Solving gives $3x=15$, so $x=5$.

Flashcard 24: Find the solution type for $7x+1=7x+4$.

Answer: No solution. Subtracting $7x$ from both sides gives $1=4$ (contradiction).

Flashcard 25: Find the solution type for $4x-7=4x-7$.

Answer: Infinitely many solutions. Subtracting $4x-7$ from both sides gives $0=0$.

Flashcard 26: Identify the number of solutions for $2(x+3)=2x+5$.

Answer: No solution. Expanding gives $2x+6=2x+5$, which simplifies to $6=5$ (false).

Flashcard 27: Identify the number of solutions for $5(x-2)=5x-10$.

Answer: Infinitely many solutions. Expanding and simplifying gives $0=0$, which is always true.

Flashcard 28: Identify the number of solutions for $3x+2=11$.

Answer: One solution. Solving gives $x=3$, a specific value.

Flashcard 29: Which result indicates exactly one solution: $x=\frac{3}{4}$, $6=6$, or $1=8$?

Answer: $x=\frac{3}{4}$. This gives $x$ a specific value, not a true/false statement.

Flashcard 30: Which result indicates no solution: $x=-2$, $0=0$, or $4=9$?

Answer: $4=9$. This is a false statement ($a=b$ where $a≠b$), creating a contradiction.