Solve Linear Equations With Rationals - 8th Grade Math
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What is the solution to $\frac{2}{5}x = 6$?
What is the solution to $\frac{2}{5}x = 6$?
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$x = 15$. Multiply both sides by $\frac{5}{2}$: $x = 6 \cdot \frac{5}{2} = 15$.
$x = 15$. Multiply both sides by $\frac{5}{2}$: $x = 6 \cdot \frac{5}{2} = 15$.
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What is the solution to $\frac{1}{3}x - 2 = 4$?
What is the solution to $\frac{1}{3}x - 2 = 4$?
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$x = 18$. Add 2, then multiply by 3: $(4+2) \cdot 3 = 18$.
$x = 18$. Add 2, then multiply by 3: $(4+2) \cdot 3 = 18$.
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What is the solution to $\frac{3}{4}x + \frac{1}{2} = 2$?
What is the solution to $\frac{3}{4}x + \frac{1}{2} = 2$?
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$x = 2$. Subtract $\frac{1}{2}$, then multiply by $\frac{4}{3}$: $\frac{3}{2} \cdot \frac{4}{3} = 2$.
$x = 2$. Subtract $\frac{1}{2}$, then multiply by $\frac{4}{3}$: $\frac{3}{2} \cdot \frac{4}{3} = 2$.
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What is the solution to $\frac{2}{3}(x - 6) = 4$?
What is the solution to $\frac{2}{3}(x - 6) = 4$?
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$x = 12$. Multiply by $\frac{3}{2}$, then add 6: $4 \cdot \frac{3}{2} + 6 = 12$.
$x = 12$. Multiply by $\frac{3}{2}$, then add 6: $4 \cdot \frac{3}{2} + 6 = 12$.
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What is the solution to $\frac{1}{2}(4x + 6) = 9$?
What is the solution to $\frac{1}{2}(4x + 6) = 9$?
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$x = 3$. Distribute, then solve: $2x + 3 = 9$, so $2x = 6$, $x = 3$.
$x = 3$. Distribute, then solve: $2x + 3 = 9$, so $2x = 6$, $x = 3$.
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What is the solution to $\frac{5}{6}x - \frac{1}{3} = \frac{1}{2}$?
What is the solution to $\frac{5}{6}x - \frac{1}{3} = \frac{1}{2}$?
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$x = 1$. Add $\frac{1}{3}$ to get $\frac{5}{6}x = \frac{5}{6}$, then $x = 1$.
$x = 1$. Add $\frac{1}{3}$ to get $\frac{5}{6}x = \frac{5}{6}$, then $x = 1$.
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What is the solution to $\frac{1}{4}x + \frac{1}{2}x = 6$?
What is the solution to $\frac{1}{4}x + \frac{1}{2}x = 6$?
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$x = 8$. Combine like terms: $\frac{3}{4}x = 6$, then $x = 8$.
$x = 8$. Combine like terms: $\frac{3}{4}x = 6$, then $x = 8$.
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What is the solution to $2(x - \frac{3}{2}) = 5$?
What is the solution to $2(x - \frac{3}{2}) = 5$?
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$x = 4$. Distribute 2, then solve: $2x - 3 = 5$, so $x = 4$.
$x = 4$. Distribute 2, then solve: $2x - 3 = 5$, so $x = 4$.
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What is the solution to $\frac{3}{5}x + 2 = \frac{1}{5}x + 6$?
What is the solution to $\frac{3}{5}x + 2 = \frac{1}{5}x + 6$?
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$x = 10$. Subtract $\frac{1}{5}x$ and 2: $\frac{2}{5}x = 4$, so $x = 10$.
$x = 10$. Subtract $\frac{1}{5}x$ and 2: $\frac{2}{5}x = 4$, so $x = 10$.
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What is the solution to $x + \frac{3}{8} = \frac{7}{8}$?
What is the solution to $x + \frac{3}{8} = \frac{7}{8}$?
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$x = \frac{1}{2}$. Subtract $\frac{3}{8}$ from both sides: $x = \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2}$.
$x = \frac{1}{2}$. Subtract $\frac{3}{8}$ from both sides: $x = \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2}$.
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What is the LCD of $\frac{1}{6}$, $\frac{1}{4}$, and $\frac{1}{3}$?
What is the LCD of $\frac{1}{6}$, $\frac{1}{4}$, and $\frac{1}{3}$?
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$12$. Find the smallest number divisible by 6, 4, and 3.
$12$. Find the smallest number divisible by 6, 4, and 3.
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What is the solution to $\frac{1}{2}x - \frac{3}{4} = \frac{1}{4}x + \frac{1}{2}$?
What is the solution to $\frac{1}{2}x - \frac{3}{4} = \frac{1}{4}x + \frac{1}{2}$?
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$x = 5$. Subtract $\frac{1}{4}x$, add $\frac{3}{4}$: $\frac{1}{4}x = \frac{5}{4}$, so $x = 5$.
$x = 5$. Subtract $\frac{1}{4}x$, add $\frac{3}{4}$: $\frac{1}{4}x = \frac{5}{4}$, so $x = 5$.
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What is the solution to $\frac{x}{3} + \frac{x}{6} = 5$?
What is the solution to $\frac{x}{3} + \frac{x}{6} = 5$?
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$x = 10$. Combine fractions: $\frac{2x}{6} + \frac{x}{6} = \frac{3x}{6} = \frac{x}{2} = 5$.
$x = 10$. Combine fractions: $\frac{2x}{6} + \frac{x}{6} = \frac{3x}{6} = \frac{x}{2} = 5$.
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What is the solution to $\frac{2}{3}x + \frac{1}{2} = \frac{1}{6}x + \frac{5}{2}$?
What is the solution to $\frac{2}{3}x + \frac{1}{2} = \frac{1}{6}x + \frac{5}{2}$?
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$x = 4$. Subtract $\frac{1}{6}x$ and $\frac{1}{2}$: $\frac{1}{2}x = 2$, so $x = 4$.
$x = 4$. Subtract $\frac{1}{6}x$ and $\frac{1}{2}$: $\frac{1}{2}x = 2$, so $x = 4$.
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What is the inverse operation for subtracting $\frac{7}{3}$ from $x$ in $x - \frac{7}{3}$?
What is the inverse operation for subtracting $\frac{7}{3}$ from $x$ in $x - \frac{7}{3}$?
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Add $\frac{7}{3}$. Addition undoes subtraction to isolate the variable.
Add $\frac{7}{3}$. Addition undoes subtraction to isolate the variable.
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What is the result after combining like terms: $\frac{3}{4}x - \frac{1}{2}x$?
What is the result after combining like terms: $\frac{3}{4}x - \frac{1}{2}x$?
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$\frac{1}{4}x$. Convert to common denominator: $\frac{3}{4}x - \frac{2}{4}x = \frac{1}{4}x$.
$\frac{1}{4}x$. Convert to common denominator: $\frac{3}{4}x - \frac{2}{4}x = \frac{1}{4}x$.
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What does it mean to collect like terms in $2x + 5 - x$?
What does it mean to collect like terms in $2x + 5 - x$?
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Combine terms with the same variable and exponent. Add or subtract coefficients of matching variables.
Combine terms with the same variable and exponent. Add or subtract coefficients of matching variables.
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Identify the simplified expression: $\frac{1}{2}(6x - 8)$.
Identify the simplified expression: $\frac{1}{2}(6x - 8)$.
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$3x - 4$. Distribute $\frac{1}{2}$ to both terms: $\frac{6x}{2} - \frac{8}{2}$.
$3x - 4$. Distribute $\frac{1}{2}$ to both terms: $\frac{6x}{2} - \frac{8}{2}$.
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What property lets you rewrite $3(x - 4)$ as $3x - 12$?
What property lets you rewrite $3(x - 4)$ as $3x - 12$?
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Distributive property. Multiply each term inside parentheses by the outside factor.
Distributive property. Multiply each term inside parentheses by the outside factor.
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What is $x$ in the equation $x+ rac{2}{3}= rac{5}{3}$?
What is $x$ in the equation $x+ rac{2}{3}= rac{5}{3}$?
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$x=1$. Subtract $ rac{2}{3}$ from both sides.
$x=1$. Subtract $ rac{2}{3}$ from both sides.
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What is $x$ in the equation $3(x-4)=15$?
What is $x$ in the equation $3(x-4)=15$?
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$x=9$. Distribute, add 12, then divide by 3.
$x=9$. Distribute, add 12, then divide by 3.
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What is $x$ in the equation $3x-2(x+4)=1$?
What is $x$ in the equation $3x-2(x+4)=1$?
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$x=9$. Distribute, combine like terms, then solve.
$x=9$. Distribute, combine like terms, then solve.
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What is $x$ in the equation $ rac{2}{5}x- rac{1}{5}=1$?
What is $x$ in the equation $ rac{2}{5}x- rac{1}{5}=1$?
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$x=3$. Add $ rac{1}{5}$, then multiply by $ rac{5}{2}$.
$x=3$. Add $ rac{1}{5}$, then multiply by $ rac{5}{2}$.
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What is $x$ in the equation $ rac{2}{3}(x-3)+1=3$?
What is $x$ in the equation $ rac{2}{3}(x-3)+1=3$?
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$x=6$. Distribute $ rac{2}{3}$, then isolate $x$.
$x=6$. Distribute $ rac{2}{3}$, then isolate $x$.
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What is the first step to solve $3(x-4)=15$?
What is the first step to solve $3(x-4)=15$?
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Distribute: $3x-12=15$. Apply $3(x-4)=3x-12$ to expand the left side.
Distribute: $3x-12=15$. Apply $3(x-4)=3x-12$ to expand the left side.
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What is $x$ in the equation $x- rac{5}{6}= rac{1}{6}$?
What is $x$ in the equation $x- rac{5}{6}= rac{1}{6}$?
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$x=1$. Add $ rac{5}{6}$ to both sides to get $x= rac{6}{6}=1$.
$x=1$. Add $ rac{5}{6}$ to both sides to get $x= rac{6}{6}=1$.
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What property lets you multiply both sides of $a=b$ by the same nonzero number $c$?
What property lets you multiply both sides of $a=b$ by the same nonzero number $c$?
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Multiplication Property of Equality. If $a=b$, then $ac=bc$ for any nonzero $c$.
Multiplication Property of Equality. If $a=b$, then $ac=bc$ for any nonzero $c$.
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What does it mean to solve a linear equation in one variable?
What does it mean to solve a linear equation in one variable?
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Find the value of $x$ that makes the equation true. The solution is the value that satisfies the equation.
Find the value of $x$ that makes the equation true. The solution is the value that satisfies the equation.
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What is $x$ in the equation $ rac{1}{2}(x+6)=5$?
What is $x$ in the equation $ rac{1}{2}(x+6)=5$?
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$x=4$. Multiply both sides by 2, then subtract 6.
$x=4$. Multiply both sides by 2, then subtract 6.
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What is $x$ in the equation $5-2(x+1)=1$?
What is $x$ in the equation $5-2(x+1)=1$?
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$x=1$. Distribute $-2$, then solve for $x$.
$x=1$. Distribute $-2$, then solve for $x$.
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