Explaining and Justifying Equation Solving Steps - Algebra
Card 1 of 30
Identify the solution of $5(x-2)=15$.
Identify the solution of $5(x-2)=15$.
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$x=5$. Divide by $5$, then add $2$ to get $x = 5$.
$x=5$. Divide by $5$, then add $2$ to get $x = 5$.
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Identify the solution of $7-2x=1$.
Identify the solution of $7-2x=1$.
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$x=3$. Subtract $7$, divide by $-2$ to get $x = 3$.
$x=3$. Subtract $7$, divide by $-2$ to get $x = 3$.
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Identify the solution of $2(x+4)=18$.
Identify the solution of $2(x+4)=18$.
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$x=5$. Divide by $2$, then subtract $4$ to get $x = 5$.
$x=5$. Divide by $2$, then subtract $4$ to get $x = 5$.
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Identify the solution of $9=3x+0$.
Identify the solution of $9=3x+0$.
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$x=3$. Divide both sides by $3$ to get $x = 3$.
$x=3$. Divide both sides by $3$ to get $x = 3$.
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Identify the solution of $0.5x=6$.
Identify the solution of $0.5x=6$.
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$x=12$. Divide both sides by $0.5$ to get $x = 12$.
$x=12$. Divide both sides by $0.5$ to get $x = 12$.
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Identify the solution of $0.2x+1=3$.
Identify the solution of $0.2x+1=3$.
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$x=10$. Subtract $1$, then divide by $0.2$ to get $x = 10$.
$x=10$. Subtract $1$, then divide by $0.2$ to get $x = 10$.
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Identify the solution of $-3x=12$.
Identify the solution of $-3x=12$.
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$x=-4$. Divide both sides by $-3$ to get $x = -4$.
$x=-4$. Divide both sides by $-3$ to get $x = -4$.
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Identify the solution of $-2x+5=-1$.
Identify the solution of $-2x+5=-1$.
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$x=3$. Subtract $5$, then divide by $-2$ to get $x = 3$.
$x=3$. Subtract $5$, then divide by $-2$ to get $x = 3$.
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Identify the solution of $3x+5=20$.
Identify the solution of $3x+5=20$.
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$x=5$. Subtract $5$, then divide by $3$ to get $x = 5$.
$x=5$. Subtract $5$, then divide by $3$ to get $x = 5$.
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Identify the solution of $4x=28$.
Identify the solution of $4x=28$.
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$x=7$. Divide both sides by $4$ to get $x = 7$.
$x=7$. Divide both sides by $4$ to get $x = 7$.
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Which property justifies going from $2x=4$ to $x=2$?
Which property justifies going from $2x=4$ to $x=2$?
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Division Property of Equality. Dividing by $2$ isolates the variable $x$.
Division Property of Equality. Dividing by $2$ isolates the variable $x$.
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Which property justifies going from $2x+6=10$ to $2x=4$?
Which property justifies going from $2x+6=10$ to $2x=4$?
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Subtraction Property of Equality. Subtracting $6$ from both sides removes the constant term.
Subtraction Property of Equality. Subtracting $6$ from both sides removes the constant term.
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Which step is valid to justify going from $x+8=3$ to $x=-5$?
Which step is valid to justify going from $x+8=3$ to $x=-5$?
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Subtract $8$ from both sides. This operation transforms the equation from $x + 8 = 3$ to $x = -5$.
Subtract $8$ from both sides. This operation transforms the equation from $x + 8 = 3$ to $x = -5$.
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What is the most direct way to check that $x=4$ solves $2x+1=9$?
What is the most direct way to check that $x=4$ solves $2x+1=9$?
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Substitute $x=4$ and verify $9=9$. Substitution confirms the solution by making both sides equal.
Substitute $x=4$ and verify $9=9$. Substitution confirms the solution by making both sides equal.
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Which property justifies rewriting $x+3x$ as $4x$ while solving an equation?
Which property justifies rewriting $x+3x$ as $4x$ while solving an equation?
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Combine like terms (distributive idea). Like terms have the same variable part and can be combined.
Combine like terms (distributive idea). Like terms have the same variable part and can be combined.
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Identify the solution of $ rac{x}{2}+ rac{x}{3}=5$.
Identify the solution of $ rac{x}{2}+ rac{x}{3}=5$.
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$x=6$. After clearing denominators: $3x + 2x = 30$, so $x = 6$.
$x=6$. After clearing denominators: $3x + 2x = 30$, so $x = 6$.
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Which step correctly clears denominators in $ rac{x}{2}+ rac{x}{3}=5$?
Which step correctly clears denominators in $ rac{x}{2}+ rac{x}{3}=5$?
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Multiply both sides by $6$. The LCD of $2$ and $3$ is $6$, so multiply by $6$.
Multiply both sides by $6$. The LCD of $2$ and $3$ is $6$, so multiply by $6$.
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Identify the property used to justify from $x+2=7$ to $x=5$.
Identify the property used to justify from $x+2=7$ to $x=5$.
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Subtraction Property of Equality. Subtracting $2$ from both sides isolates the variable.
Subtraction Property of Equality. Subtracting $2$ from both sides isolates the variable.
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Identify the property used to justify from $3(x+2)=21$ to $x+2=7$.
Identify the property used to justify from $3(x+2)=21$ to $x+2=7$.
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Division Property of Equality. Dividing both sides by $3$ simplifies the parenthetical expression.
Division Property of Equality. Dividing both sides by $3$ simplifies the parenthetical expression.
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Identify the property used to justify from $x-4=9$ to $x-4+4=9+4$.
Identify the property used to justify from $x-4=9$ to $x-4+4=9+4$.
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Addition Property of Equality. Adding $4$ to both sides removes the subtracted term.
Addition Property of Equality. Adding $4$ to both sides removes the subtracted term.
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Find and correct the invalid step: divide both sides of $x\cdot 0=5\cdot 0$ by $0$ to get $x=5$.
Find and correct the invalid step: divide both sides of $x\cdot 0=5\cdot 0$ by $0$ to get $x=5$.
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Division by $0$ is invalid. Division by zero is undefined in mathematics.
Division by $0$ is invalid. Division by zero is undefined in mathematics.
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Find and correct the invalid step: from $x=3$ conclude $ rac{1}{x}= rac{1}{3}$ without a condition.
Find and correct the invalid step: from $x=3$ conclude $ rac{1}{x}= rac{1}{3}$ without a condition.
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Valid only if $x\ne 0$. The reciprocal operation requires the denominator to be nonzero.
Valid only if $x\ne 0$. The reciprocal operation requires the denominator to be nonzero.
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What property states that if $a=b$ and $b=c$, then $a=c$?
What property states that if $a=b$ and $b=c$, then $a=c$?
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Transitive Property of Equality. This property chains equal expressions together.
Transitive Property of Equality. This property chains equal expressions together.
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What property states that if $a=b$, then $a$ may be replaced by $b$ in any expression?
What property states that if $a=b$, then $a$ may be replaced by $b$ in any expression?
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Substitution Property of Equality. This property allows replacing equal values in expressions.
Substitution Property of Equality. This property allows replacing equal values in expressions.
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What property states that if $a=b$, then $a+c=b+c$ for any real $c$?
What property states that if $a=b$, then $a+c=b+c$ for any real $c$?
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Addition Property of Equality. This is the formal statement of adding the same value to both sides.
Addition Property of Equality. This is the formal statement of adding the same value to both sides.
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What property states that if $a=b$, then $a-c=b-c$ for any real $c$?
What property states that if $a=b$, then $a-c=b-c$ for any real $c$?
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Subtraction Property of Equality. This is the formal statement of subtracting the same value from both sides.
Subtraction Property of Equality. This is the formal statement of subtracting the same value from both sides.
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What restriction is required to use the Division Property of Equality on $ rac{a}{c}= rac{b}{c}$?
What restriction is required to use the Division Property of Equality on $ rac{a}{c}= rac{b}{c}$?
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$c\ne 0$. Division by zero is undefined, so $c$ cannot equal zero.
$c\ne 0$. Division by zero is undefined, so $c$ cannot equal zero.
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What restriction is required before multiplying an equation by $ rac{1}{x}$?
What restriction is required before multiplying an equation by $ rac{1}{x}$?
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$x\ne 0$. Multiplying by $\frac{1}{x}$ requires $x \ne 0$ since $\frac{1}{0}$ is undefined.
$x\ne 0$. Multiplying by $\frac{1}{x}$ requires $x \ne 0$ since $\frac{1}{0}$ is undefined.
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What is the standard goal when solving a linear equation in one variable?
What is the standard goal when solving a linear equation in one variable?
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Isolate the variable (get $x$ alone). This creates an equation in the form $x = \text{value}$.
Isolate the variable (get $x$ alone). This creates an equation in the form $x = \text{value}$.
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What term describes an operation that reverses another operation when solving equations?
What term describes an operation that reverses another operation when solving equations?
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Inverse operation. These operations cancel each other out to isolate variables.
Inverse operation. These operations cancel each other out to isolate variables.
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