Equations With One Variable - PSAT Math
Card 1 of 30
What is the solution to the equation $x^2=49$?
What is the solution to the equation $x^2=49$?
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$x=7$ or $x=-7$. Take square root of both sides: $x = ±sqrt{49} = ±7$.
$x=7$ or $x=-7$. Take square root of both sides: $x = ±sqrt{49} = ±7$.
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What is the solution to the equation $ rac{x-5}{3}=4$?
What is the solution to the equation $ rac{x-5}{3}=4$?
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$x=17$. Multiply by 3, then add 5: $x - 5 = 12$, so $x = 17$.
$x=17$. Multiply by 3, then add 5: $x - 5 = 12$, so $x = 17$.
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What is the solution to the equation $0.2x=8$?
What is the solution to the equation $0.2x=8$?
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$x=40$. Divide by 0.2 (same as multiply by 5): $x = 8 ÷ 0.2 = 40$.
$x=40$. Divide by 0.2 (same as multiply by 5): $x = 8 ÷ 0.2 = 40$.
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What is the solution to the equation $4x+6=2x+18$?
What is the solution to the equation $4x+6=2x+18$?
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$x=6$. Subtract $2x$ and 6 from both sides: $2x = 12$, so $x = 6$.
$x=6$. Subtract $2x$ and 6 from both sides: $2x = 12$, so $x = 6$.
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What operation property justifies adding the same number to both sides of $a=b$?
What operation property justifies adding the same number to both sides of $a=b$?
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Addition Property of Equality. States that if $a=b$, then $a+c=b+c$ for any number $c$.
Addition Property of Equality. States that if $a=b$, then $a+c=b+c$ for any number $c$.
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What operation property justifies multiplying both sides of $a=b$ by the same nonzero number?
What operation property justifies multiplying both sides of $a=b$ by the same nonzero number?
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Multiplication Property of Equality. States that if $a=b$, then $ac=bc$ for any nonzero number $c$.
Multiplication Property of Equality. States that if $a=b$, then $ac=bc$ for any nonzero number $c$.
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What is the solution to the equation $x+7=19$?
What is the solution to the equation $x+7=19$?
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$x=12$. Subtract 7 from both sides: $x = 19 - 7 = 12$.
$x=12$. Subtract 7 from both sides: $x = 19 - 7 = 12$.
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What is the solution to the equation $5x=35$?
What is the solution to the equation $5x=35$?
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$x=7$. Divide both sides by 5: $x = 35 ÷ 5 = 7$.
$x=7$. Divide both sides by 5: $x = 35 ÷ 5 = 7$.
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What is the solution to the equation $2(x+3)=18$?
What is the solution to the equation $2(x+3)=18$?
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$x=6$. Divide by 2, then subtract 3: $x + 3 = 9$, so $x = 6$.
$x=6$. Divide by 2, then subtract 3: $x + 3 = 9$, so $x = 6$.
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What is the solution to the equation $|3x|=12$?
What is the solution to the equation $|3x|=12$?
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$x=4$ or $x=-4$. Divide by 3: $|x| = 4$, so $x = 4$ or $x = -4$.
$x=4$ or $x=-4$. Divide by 3: $|x| = 4$, so $x = 4$ or $x = -4$.
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What is the solution to the equation $|x-2|=5$?
What is the solution to the equation $|x-2|=5$?
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$x=7$ or $x=-3$. Absolute value gives two cases: $x - 2 = 5$ or $x - 2 = -5$.
$x=7$ or $x=-3$. Absolute value gives two cases: $x - 2 = 5$ or $x - 2 = -5$.
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What is the solution to the equation $(x-3)^2=16$?
What is the solution to the equation $(x-3)^2=16$?
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$x=7$ or $x=-1$. Take square root: $x - 3 = ±4$, so $x = 7$ or $x = -1$.
$x=7$ or $x=-1$. Take square root: $x - 3 = ±4$, so $x = 7$ or $x = -1$.
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What is the solution to the equation $ rac{2x+1}{5}=3$?
What is the solution to the equation $ rac{2x+1}{5}=3$?
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$x=7$. Multiply by 5, then solve: $2x + 1 = 15$, so $x = 7$.
$x=7$. Multiply by 5, then solve: $2x + 1 = 15$, so $x = 7$.
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What is the solution to the equation $ rac{x}{4}=9$?
What is the solution to the equation $ rac{x}{4}=9$?
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$x=36$. Multiply both sides by 4: $x = 9 × 4 = 36$.
$x=36$. Multiply both sides by 4: $x = 9 × 4 = 36$.
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What is the solution to the equation $3x-5=16$?
What is the solution to the equation $3x-5=16$?
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$x=7$. Add 5 to both sides, then divide by 3: $3x = 21$, so $x = 7$.
$x=7$. Add 5 to both sides, then divide by 3: $3x = 21$, so $x = 7$.
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What is the solution to the equation $7-2x=15$?
What is the solution to the equation $7-2x=15$?
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$x=-4$. Subtract 7, then divide by -2: $-2x = 8$, so $x = -4$.
$x=-4$. Subtract 7, then divide by -2: $-2x = 8$, so $x = -4$.
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What is the solution to the equation $ rac{3}{x}=6$?
What is the solution to the equation $ rac{3}{x}=6$?
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$x= rac{1}{2}$. Cross multiply: $3 = 6x$, so $x = rac{3}{6} = rac{1}{2}$.
$x= rac{1}{2}$. Cross multiply: $3 = 6x$, so $x = rac{3}{6} = rac{1}{2}$.
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What is the solution set of $3(x-1)=3x+2$?
What is the solution set of $3(x-1)=3x+2$?
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No solution. Expanding gives $3x - 3 = 3x + 2$, which simplifies to $-3 = 2$ (false).
No solution. Expanding gives $3x - 3 = 3x + 2$, which simplifies to $-3 = 2$ (false).
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What is the solution set of $2(x+1)=2x+2$?
What is the solution set of $2(x+1)=2x+2$?
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All real numbers. Expanding gives $2x + 2 = 2x + 2$, which is always true.
All real numbers. Expanding gives $2x + 2 = 2x + 2$, which is always true.
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What is the solution to $ rac{3}{x}=6$ with $x\ne 0$?
What is the solution to $ rac{3}{x}=6$ with $x\ne 0$?
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$x=\frac{1}{2}$. Cross multiply: $3 = 6x$, so $x = rac{3}{6} = rac{1}{2}$.
$x=\frac{1}{2}$. Cross multiply: $3 = 6x$, so $x = rac{3}{6} = rac{1}{2}$.
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What is the solution of $5x = 35$?
What is the solution of $5x = 35$?
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$x = 7$. Divide both sides by 5: $35 ÷ 5 = 7$.
$x = 7$. Divide both sides by 5: $35 ÷ 5 = 7$.
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What is the solution to $3(x+2)=18$?
What is the solution to $3(x+2)=18$?
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$x=4$. Divide by $3$ to get $x+2=6$, then subtract $2$.
$x=4$. Divide by $3$ to get $x+2=6$, then subtract $2$.
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What is the solution to $ rac{x}{2}+ rac{x}{3}=10$?
What is the solution to $ rac{x}{2}+ rac{x}{3}=10$?
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$x=12$. Common denominator 6: $ rac{3x}{6} + rac{2x}{6} = 10$, so $ rac{5x}{6} = 10$, thus $x = 12$.
$x=12$. Common denominator 6: $ rac{3x}{6} + rac{2x}{6} = 10$, so $ rac{5x}{6} = 10$, thus $x = 12$.
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What is the solution to $ rac{x-2}{5}=3$?
What is the solution to $ rac{x-2}{5}=3$?
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$x=17$. Multiply by 5, then add 2: $x - 2 = 15$, so $x = 17$.
$x=17$. Multiply by 5, then add 2: $x - 2 = 15$, so $x = 17$.
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What is the solution to $0.5x+1=4$?
What is the solution to $0.5x+1=4$?
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$x=6$. Subtract 1, then multiply by 2: $0.5x = 3$, so $x = 6$.
$x=6$. Subtract 1, then multiply by 2: $0.5x = 3$, so $x = 6$.
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What is $x$ if $0.2x=6$?
What is $x$ if $0.2x=6$?
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$x=30$. Divide both sides by $0.2$: $x = 6 ÷ 0.2 = 30$.
$x=30$. Divide both sides by $0.2$: $x = 6 ÷ 0.2 = 30$.
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What is the solution to $x^2=49$?
What is the solution to $x^2=49$?
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$x=7$ or $x=-7$. Take square root of both sides: $x = pmsqrt{49} = pm 7$.
$x=7$ or $x=-7$. Take square root of both sides: $x = pmsqrt{49} = pm 7$.
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What is the solution to $3x-5=16$?
What is the solution to $3x-5=16$?
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$x=7$. Add 5 to both sides, then divide by 3: $21÷3=7$.
$x=7$. Add 5 to both sides, then divide by 3: $21÷3=7$.
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What is the solution to $|2x+1|=7$?
What is the solution to $|2x+1|=7$?
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$x=3$ or $x=-4$. Set $2x + 1 = 7$ or $2x + 1 = -7$, solving gives $x = 3$ or $x = -4$.
$x=3$ or $x=-4$. Set $2x + 1 = 7$ or $2x + 1 = -7$, solving gives $x = 3$ or $x = -4$.
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What is the solution set of $|x-3|=5$?
What is the solution set of $|x-3|=5$?
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$x=8$ or $x=-2$. Absolute value equation: $x - 3 = 5$ or $x - 3 = -5$.
$x=8$ or $x=-2$. Absolute value equation: $x - 3 = 5$ or $x - 3 = -5$.
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