Classify Solutions to Linear Equations - 8th Grade Math
Card 1 of 30
Identify the solution type of $8x=8x-4$.
Identify the solution type of $8x=8x-4$.
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No solution. Subtracting $8x$ from both sides gives $0=-4$, which is false.
No solution. Subtracting $8x$ from both sides gives $0=-4$, which is false.
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Which result shows exactly one solution: $x=0$, $6=6$, or $2=5$?
Which result shows exactly one solution: $x=0$, $6=6$, or $2=5$?
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$x=0$. This gives one specific value for $x$ ($x=a$ form).
$x=0$. This gives one specific value for $x$ ($x=a$ form).
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Identify the solution type for $3x+5=3x+2$ after simplifying.
Identify the solution type for $3x+5=3x+2$ after simplifying.
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No solutions. Subtracting $3x$ from both sides gives $5=2$, which is false.
No solutions. Subtracting $3x$ from both sides gives $5=2$, which is false.
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What is the solution to $7-2x=1$?
What is the solution to $7-2x=1$?
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$x=3$. Subtract $7$, divide by $-2$.
$x=3$. Subtract $7$, divide by $-2$.
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What is the solution to $\frac{x}{3}+2=5$?
What is the solution to $\frac{x}{3}+2=5$?
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$x=9$. Subtract $2$, multiply by $3$.
$x=9$. Subtract $2$, multiply by $3$.
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Identify the solution type for $4(x-2)=4x-8$ after simplifying.
Identify the solution type for $4(x-2)=4x-8$ after simplifying.
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Infinitely many solutions. Expanding gives $4x-8=4x-8$, which is always true.
Infinitely many solutions. Expanding gives $4x-8=4x-8$, which is always true.
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Identify the solution type for $2x+7=17$ after simplifying.
Identify the solution type for $2x+7=17$ after simplifying.
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$1$ solution. Solving gives $x=5$, one specific value.
$1$ solution. Solving gives $x=5$, one specific value.
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What does the equation form $a=a$ indicate about the number of solutions?
What does the equation form $a=a$ indicate about the number of solutions?
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Infinitely many solutions. When simplified to $a=a$, the equation is always true for any $x$.
Infinitely many solutions. When simplified to $a=a$, the equation is always true for any $x$.
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Identify the solution type for $3(2x-5)=6x-15$ after simplifying.
Identify the solution type for $3(2x-5)=6x-15$ after simplifying.
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Infinitely many solutions. Expanding gives $6x-15=6x-15$, which is always true.
Infinitely many solutions. Expanding gives $6x-15=6x-15$, which is always true.
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Identify the solution type for $8x=8x+6$ after simplifying.
Identify the solution type for $8x=8x+6$ after simplifying.
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No solutions. Subtracting $8x$ gives $0=6$, which is false.
No solutions. Subtracting $8x$ gives $0=6$, which is false.
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Identify the solution type for $9x+1=9x-4$ after simplifying.
Identify the solution type for $9x+1=9x-4$ after simplifying.
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No solutions. Subtracting $9x$ gives $1=-4$, which is false.
No solutions. Subtracting $9x$ gives $1=-4$, which is false.
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Identify the solution type for $6x-3=6x-3$ after simplifying.
Identify the solution type for $6x-3=6x-3$ after simplifying.
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Infinitely many solutions. Both sides are identical, so the equation is always true.
Infinitely many solutions. Both sides are identical, so the equation is always true.
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What does the equation form $x=a$ indicate about the number of solutions?
What does the equation form $x=a$ indicate about the number of solutions?
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$1$ solution. When simplified to $x=a$, the variable equals one specific value.
$1$ solution. When simplified to $x=a$, the variable equals one specific value.
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What is the solution to $2(x+4)=18$?
What is the solution to $2(x+4)=18$?
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$x=5$. Expand to get $2x+8=18$, then solve.
$x=5$. Expand to get $2x+8=18$, then solve.
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Identify the solution type for $\frac{x}{2}+1=\frac{x}{2}+1$ after simplifying.
Identify the solution type for $\frac{x}{2}+1=\frac{x}{2}+1$ after simplifying.
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Infinitely many solutions. Both sides are identical, so the equation is always true.
Infinitely many solutions. Both sides are identical, so the equation is always true.
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What does the equation form $a=b$ with $a\ne b$ indicate about the number of solutions?
What does the equation form $a=b$ with $a\ne b$ indicate about the number of solutions?
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No solutions. When simplified to $a=b$ where $a≠b$, the equation is never true.
No solutions. When simplified to $a=b$ where $a≠b$, the equation is never true.
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Which result shows infinitely many solutions: $x=5$, $7=7$, or $3=9$?
Which result shows infinitely many solutions: $x=5$, $7=7$, or $3=9$?
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$7=7$. This is a true statement ($a=a$ form), so any value of $x$ works.
$7=7$. This is a true statement ($a=a$ form), so any value of $x$ works.
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Which result shows no solutions: $x=-2$, $4=4$, or $8=1$?
Which result shows no solutions: $x=-2$, $4=4$, or $8=1$?
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$8=1$. This is a false statement ($a=b$ form where $a≠b$).
$8=1$. This is a false statement ($a=b$ form where $a≠b$).
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Identify the solution type for $\frac{3}{4}x=6$.
Identify the solution type for $\frac{3}{4}x=6$.
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One solution. Multiply both sides by $ rac{4}{3}$ to get $x=8$.
One solution. Multiply both sides by $ rac{4}{3}$ to get $x=8$.
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Which equation has infinitely many solutions: $5x=5x+2$ or $7(x-1)=7x-7$?
Which equation has infinitely many solutions: $5x=5x+2$ or $7(x-1)=7x-7$?
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$7(x-1)=7x-7$. The second expands to $7x-7=7x-7$, an identity.
$7(x-1)=7x-7$. The second expands to $7x-7=7x-7$, an identity.
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Transform $8x-2=8x+1$ to one of the forms $x=a$, $a=a$, or $a=b$.
Transform $8x-2=8x+1$ to one of the forms $x=a$, $a=a$, or $a=b$.
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$-2=1$ (an $a=b$ form). Subtracting $8x$ from both sides gives this contradiction.
$-2=1$ (an $a=b$ form). Subtracting $8x$ from both sides gives this contradiction.
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Transform $6x+5=6x+5$ to one of the forms $x=a$, $a=a$, or $a=b$.
Transform $6x+5=6x+5$ to one of the forms $x=a$, $a=a$, or $a=b$.
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$0=0$ (an $a=a$ form). Subtracting $6x+5$ from both sides gives this identity.
$0=0$ (an $a=a$ form). Subtracting $6x+5$ from both sides gives this identity.
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Find the solution type for $9x-3=6x+12$.
Find the solution type for $9x-3=6x+12$.
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One solution. Solving gives $3x=15$, so $x=5$.
One solution. Solving gives $3x=15$, so $x=5$.
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Find the solution type for $7x+1=7x+4$.
Find the solution type for $7x+1=7x+4$.
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No solution. Subtracting $7x$ from both sides gives $1=4$ (contradiction).
No solution. Subtracting $7x$ from both sides gives $1=4$ (contradiction).
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Find the solution type for $4x-7=4x-7$.
Find the solution type for $4x-7=4x-7$.
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Infinitely many solutions. Subtracting $4x-7$ from both sides gives $0=0$.
Infinitely many solutions. Subtracting $4x-7$ from both sides gives $0=0$.
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Identify the number of solutions for $2(x+3)=2x+5$.
Identify the number of solutions for $2(x+3)=2x+5$.
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No solution. Expanding gives $2x+6=2x+5$, which simplifies to $6=5$ (false).
No solution. Expanding gives $2x+6=2x+5$, which simplifies to $6=5$ (false).
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Identify the number of solutions for $5(x-2)=5x-10$.
Identify the number of solutions for $5(x-2)=5x-10$.
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Infinitely many solutions. Expanding and simplifying gives $0=0$, which is always true.
Infinitely many solutions. Expanding and simplifying gives $0=0$, which is always true.
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Identify the number of solutions for $3x+2=11$.
Identify the number of solutions for $3x+2=11$.
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One solution. Solving gives $x=3$, a specific value.
One solution. Solving gives $x=3$, a specific value.
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Which result indicates exactly one solution: $x=\frac{3}{4}$, $6=6$, or $1=8$?
Which result indicates exactly one solution: $x=\frac{3}{4}$, $6=6$, or $1=8$?
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$x=\frac{3}{4}$. This gives $x$ a specific value, not a true/false statement.
$x=\frac{3}{4}$. This gives $x$ a specific value, not a true/false statement.
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Which result indicates no solution: $x=-2$, $0=0$, or $4=9$?
Which result indicates no solution: $x=-2$, $0=0$, or $4=9$?
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$4=9$. This is a false statement ($a=b$ where $a≠b$), creating a contradiction.
$4=9$. This is a false statement ($a=b$ where $a≠b$), creating a contradiction.
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