Rearranging Formulas to Highlight Quantities - Algebra 2
Card 1 of 30
What is $x$ when you solve $y = \frac{ax + b}{c}$ for $x$ (with $a \ne 0$, $c \ne 0$)?
What is $x$ when you solve $y = \frac{ax + b}{c}$ for $x$ (with $a \ne 0$, $c \ne 0$)?
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$x = \frac{cy - b}{a}$. Multiply by $c$, subtract $b$, then divide by $a$.
$x = \frac{cy - b}{a}$. Multiply by $c$, subtract $b$, then divide by $a$.
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What is $I$ when you solve Ohm's law $V = IR$ for $I$ (with $R \ne 0$)?
What is $I$ when you solve Ohm's law $V = IR$ for $I$ (with $R \ne 0$)?
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$I = \frac{V}{R}$. Divide both sides by $R$ to isolate current.
$I = \frac{V}{R}$. Divide both sides by $R$ to isolate current.
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What is $b$ when you solve triangle area $A = \frac{1}{2}bh$ for $b$ (with $h \ne 0$)?
What is $b$ when you solve triangle area $A = \frac{1}{2}bh$ for $b$ (with $h \ne 0$)?
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$b = \frac{2A}{h}$. Multiply by $2$, then divide by $h$.
$b = \frac{2A}{h}$. Multiply by $2$, then divide by $h$.
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What is $x$ when you solve $y = \frac{a}{x} + b$ for $x$ (with $y \ne b$)?
What is $x$ when you solve $y = \frac{a}{x} + b$ for $x$ (with $y \ne b$)?
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$x = \frac{a}{y - b}$. Subtract $b$, then divide $a$ by the result.
$x = \frac{a}{y - b}$. Subtract $b$, then divide $a$ by the result.
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What is $x$ when you solve $ax^2 = b$ for $x$ (with $a \ne 0$)?
What is $x$ when you solve $ax^2 = b$ for $x$ (with $a \ne 0$)?
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$x = \pm\sqrt{\frac{b}{a}}$. Divide by $a$, then take square root with $\pm$.
$x = \pm\sqrt{\frac{b}{a}}$. Divide by $a$, then take square root with $\pm$.
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What is $k$ when you solve $y = a(x - h)^2 + k$ for $k$?
What is $k$ when you solve $y = a(x - h)^2 + k$ for $k$?
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$k = y - a(x - h)^2$. Subtract the squared term from both sides.
$k = y - a(x - h)^2$. Subtract the squared term from both sides.
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What is $P$ when you solve $A = P(1 + rt)$ for $P$ (assume $1+rt \ne 0$)?
What is $P$ when you solve $A = P(1 + rt)$ for $P$ (assume $1+rt \ne 0$)?
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$P = \frac{A}{1 + rt}$. Divide both sides by $(1 + rt)$.
$P = \frac{A}{1 + rt}$. Divide both sides by $(1 + rt)$.
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What is $I$ when you solve Ohm's law $V = IR$ for $I$ (with $R \ne 0$)?
What is $I$ when you solve Ohm's law $V = IR$ for $I$ (with $R \ne 0$)?
Tap to reveal answer
$I = \frac{V}{R}$. Divide both sides by $R$ to isolate current.
$I = \frac{V}{R}$. Divide both sides by $R$ to isolate current.
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What is $V$ when you solve Ohm's law $V = IR$ for $V$?
What is $V$ when you solve Ohm's law $V = IR$ for $V$?
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$V = IR$. No rearrangement needed; $V$ is already isolated.
$V = IR$. No rearrangement needed; $V$ is already isolated.
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What is $W$ when you solve $P = 2L + 2W$ for $W$ (treat $P,L$ as constants)?
What is $W$ when you solve $P = 2L + 2W$ for $W$ (treat $P,L$ as constants)?
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$W = \frac{P - 2L}{2}$. Subtract $2L$, then divide by $2$.
$W = \frac{P - 2L}{2}$. Subtract $2L$, then divide by $2$.
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What is $r$ when you solve the circle area formula $A = \pi r^2$ for $r$?
What is $r$ when you solve the circle area formula $A = \pi r^2$ for $r$?
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$r = \sqrt{\frac{A}{\pi}}$. Divide by $\pi$, then take the square root.
$r = \sqrt{\frac{A}{\pi}}$. Divide by $\pi$, then take the square root.
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What is $h$ when you solve the cylinder volume formula $V = \pi r^2 h$ for $h$?
What is $h$ when you solve the cylinder volume formula $V = \pi r^2 h$ for $h$?
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$h = \frac{V}{\pi r^2}$. Divide both sides by $\pi r^2$.
$h = \frac{V}{\pi r^2}$. Divide both sides by $\pi r^2$.
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What is $r$ when you solve $V = \pi r^2 h$ for $r$ (assume $h>0$)?
What is $r$ when you solve $V = \pi r^2 h$ for $r$ (assume $h>0$)?
Tap to reveal answer
$r = \sqrt{\frac{V}{\pi h}}$. Divide by $\pi h$, then take the square root.
$r = \sqrt{\frac{V}{\pi h}}$. Divide by $\pi h$, then take the square root.
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What is $b$ when you solve triangle area $A = \frac{1}{2}bh$ for $b$ (with $h \ne 0$)?
What is $b$ when you solve triangle area $A = \frac{1}{2}bh$ for $b$ (with $h \ne 0$)?
Tap to reveal answer
$b = \frac{2A}{h}$. Multiply by $2$, then divide by $h$.
$b = \frac{2A}{h}$. Multiply by $2$, then divide by $h$.
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What is $h$ when you solve triangle area $A = \frac{1}{2}bh$ for $h$ (with $b \ne 0$)?
What is $h$ when you solve triangle area $A = \frac{1}{2}bh$ for $h$ (with $b \ne 0$)?
Tap to reveal answer
$h = \frac{2A}{b}$. Multiply by $2$, then divide by $b$.
$h = \frac{2A}{b}$. Multiply by $2$, then divide by $b$.
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What is $r$ when you solve circumference $C = 2\pi r$ for $r$?
What is $r$ when you solve circumference $C = 2\pi r$ for $r$?
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$r = \frac{C}{2\pi}$. Divide both sides by $2\pi$.
$r = \frac{C}{2\pi}$. Divide both sides by $2\pi$.
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What is $r$ when you solve $d = rt$ for $r$ (with $t \ne 0$)?
What is $r$ when you solve $d = rt$ for $r$ (with $t \ne 0$)?
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$r = \frac{d}{t}$. Divide both sides by $t$.
$r = \frac{d}{t}$. Divide both sides by $t$.
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What is $t$ when you solve $A = P(1 + rt)$ for $t$ (with $Pr \ne 0$)?
What is $t$ when you solve $A = P(1 + rt)$ for $t$ (with $Pr \ne 0$)?
Tap to reveal answer
$t = \frac{\frac{A}{P} - 1}{r}$. Divide by $P$, subtract $1$, then divide by $r$.
$t = \frac{\frac{A}{P} - 1}{r}$. Divide by $P$, subtract $1$, then divide by $r$.
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What is $r$ when you solve $A = P(1 + rt)$ for $r$ (with $Pt \ne 0$)?
What is $r$ when you solve $A = P(1 + rt)$ for $r$ (with $Pt \ne 0$)?
Tap to reveal answer
$r = \frac{\frac{A}{P} - 1}{t}$. Divide by $P$, subtract $1$, then divide by $t$.
$r = \frac{\frac{A}{P} - 1}{t}$. Divide by $P$, subtract $1$, then divide by $t$.
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What is $P$ when you solve $A = P\left(1 + \frac{r}{n}\right)^{nt}$ for $P$?
What is $P$ when you solve $A = P\left(1 + \frac{r}{n}\right)^{nt}$ for $P$?
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$P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$. Divide by the compound interest factor.
$P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$. Divide by the compound interest factor.
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What is $b$ when you solve $y = a(b^x)$ for $b$ (assume $a>0$, $y>0$)?
What is $b$ when you solve $y = a(b^x)$ for $b$ (assume $a>0$, $y>0$)?
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$b = \left(\frac{y}{a}\right)^{\frac{1}{x}}$. Take the $x$th root of $\frac{y}{a}$.
$b = \left(\frac{y}{a}\right)^{\frac{1}{x}}$. Take the $x$th root of $\frac{y}{a}$.
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What is $a$ when you solve $y = a(b^x)$ for $a$ (assume $b^x \ne 0$)?
What is $a$ when you solve $y = a(b^x)$ for $a$ (assume $b^x \ne 0$)?
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$a = \frac{y}{b^x}$. Divide both sides by $b^x$.
$a = \frac{y}{b^x}$. Divide both sides by $b^x$.
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What is $x$ when you solve $y = \log_b(x)$ for $x$ (assume $b>0$, $b\ne 1$)?
What is $x$ when you solve $y = \log_b(x)$ for $x$ (assume $b>0$, $b\ne 1$)?
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$x = b^y$. Apply the definition of logarithms: $\log_b(x) = y$ means $b^y = x$.
$x = b^y$. Apply the definition of logarithms: $\log_b(x) = y$ means $b^y = x$.
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What is $b$ when you solve $y = \log_b(x)$ for $b$ (assume $x>0$, $y \ne 0$)?
What is $b$ when you solve $y = \log_b(x)$ for $b$ (assume $x>0$, $y \ne 0$)?
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$b = x^{\frac{1}{y}}$. Rewrite as $b^y = x$, then solve for $b$.
$b = x^{\frac{1}{y}}$. Rewrite as $b^y = x$, then solve for $b$.
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What is $x$ when you solve $y = \ln(x)$ for $x$?
What is $x$ when you solve $y = \ln(x)$ for $x$?
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$x = e^y$. Apply the inverse relationship between $\ln$ and $e$.
$x = e^y$. Apply the inverse relationship between $\ln$ and $e$.
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What is $x$ when you solve $y = \sqrt{x - h}$ for $x$?
What is $x$ when you solve $y = \sqrt{x - h}$ for $x$?
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$x = y^2 + h$. Square both sides, then add $h$.
$x = y^2 + h$. Square both sides, then add $h$.
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What is $x$ when you solve $y = \sqrt{ax + b}$ for $x$ (with $a \ne 0$)?
What is $x$ when you solve $y = \sqrt{ax + b}$ for $x$ (with $a \ne 0$)?
Tap to reveal answer
$x = \frac{y^2 - b}{a}$. Square both sides, subtract $b$, then divide by $a$.
$x = \frac{y^2 - b}{a}$. Square both sides, subtract $b$, then divide by $a$.
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What is $x$ when you solve $y = (ax + b)^2$ for $x$ (with $a \ne 0$)?
What is $x$ when you solve $y = (ax + b)^2$ for $x$ (with $a \ne 0$)?
Tap to reveal answer
$x = \frac{\pm\sqrt{y} - b}{a}$. Take square root of both sides, then solve for $x$.
$x = \frac{\pm\sqrt{y} - b}{a}$. Take square root of both sides, then solve for $x$.
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What is $x$ when you solve $y = \frac{ax + b}{c}$ for $x$ (with $a \ne 0$, $c \ne 0$)?
What is $x$ when you solve $y = \frac{ax + b}{c}$ for $x$ (with $a \ne 0$, $c \ne 0$)?
Tap to reveal answer
$x = \frac{cy - b}{a}$. Multiply by $c$, subtract $b$, then divide by $a$.
$x = \frac{cy - b}{a}$. Multiply by $c$, subtract $b$, then divide by $a$.
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What is $x$ when you solve $y = \frac{a}{x} + b$ for $x$ (with $y \ne b$)?
What is $x$ when you solve $y = \frac{a}{x} + b$ for $x$ (with $y \ne b$)?
Tap to reveal answer
$x = \frac{a}{y - b}$. Subtract $b$, then divide $a$ by the result.
$x = \frac{a}{y - b}$. Subtract $b$, then divide $a$ by the result.
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