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Change the Subject of an Equation

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Change the Subject of an Equation 2

Change the Subject of an Equation 2

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Question 1 of 5

1. Question
Write $d$ $d$ as the subject of the equation below

$A = \frac{1}{2} h (c + d)$ $A=1/2h(c+d)$
- 1. $d = 2 A h + c$ $d=2Ah+c$
- 2. $d = \frac{2 h}{A} - c$ $d=(2h)/A-c$
- 3. $d = 2 A h - c$ $d=2Ah-c$
- 4. $d = \frac{2 A}{h} - c$ $d=(2A)/h-c$
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equation

Multiply both sides to $2$ $2$

$A$ $A$ $=$ $=$ $\frac{1}{2} h (c + d)$ $1/2h(c+d)$

$A$ $A$ $\times 2$ $xx2$ $=$ $=$ $\frac{1}{2} h (c + d)$ $1/2h(c+d)$ $\times 2$ $xx2$

$2 A$ $2A$ $=$ $=$ $h (c + d)$ $h(c+d)$ $\frac{1}{2} \times 2$ $1/2xx2$ cancels out

Divide both sides by $h$ $h$

$2 A$ $2A$ $=$ $=$ $h (c + d)$ $h(c+d)$

$2 A$ $2A$ $\div h$ $-:h$ $=$ $=$ $h (c + d)$ $h(c+d)$ $\div h$ $-:h$

$\frac{2 A}{h}$ $(2A)/h$ $=$ $=$ $c + d$ $c+d$ $h \div h$ $h-:h$ cancels out

Finally, subtract $c$ $c$ from both sides

$\frac{2 A}{h}$ $(2A)/h$ $=$ $=$ $c + d$ $c+d$

$\frac{2 A}{h}$ $(2A)/h$ $- c$ $-c$ $=$ $=$ $c + d$ $c+d$ $- c$ $-c$

$\frac{2 A}{h} - c$ $(2A)/h-c$ $=$ $=$ $d$ $d$ $c - c$ $c-c$ cancels out

$d$ $d$ $=$ $=$ $\frac{2 A}{h} - c$ $(2A)/h-c$ Interchange the sides

$d = \frac{2 A}{h} - c$ $d=(2A)/h-c$

Question 2 of 5

2. Question

Write

x

$x$ as the subject of the equation below

G (x + y) = H (x - y)

$G(x+y)=H(x-y)$

1. $x = \frac{y (- G - H)}{G H}$ $x=(y(-G-H))/(GH)$
2. $x = \frac{y (G - H)}{H + G}$ $x=(y(G-H))/(H+G)$
3. $x = \frac{y (G + H)}{H - G}$ $x=(y(G+H))/(H-G)$
4. $x = y$ $x=y$

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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equation

Distribute

G

$G$ and

H

$H$

$G (x + y)$ $G(x+y)$	$=$ $=$	$H (x - y)$ $H(x-y)$
$G x + G y$ $Gx+Gy$	$=$ $=$	$H x - H y$ $Hx-Hy$

Leave only

x

$x$ terms on the left

$G x + G y$ $Gx+Gy$	$=$ $=$	$H x - H y$ $Hx-Hy$
$G x + G y$ $Gx+Gy$ $- H x$ $-Hx$	$=$ $=$	$H x - H y$ $Hx-Hy$ $- H x$ $-Hx$	Subtract $H x$ $Hx$ from both sides
$G x + G y - H x$ $Gx+Gy-Hx$	$=$ $=$	$- H y$ $-Hy$	$H x - H x$ $Hx-Hx$ cancels out
$G x + G y - H x$ $Gx+Gy-Hx$ $- G y$ $-Gy$	$=$ $=$	$- H y$ $-Hy$ $- G y$ $-Gy$	Subtract $G y$ $Gy$ from both sides
$G x - H x$ $Gx-Hx$	$=$ $=$	$- G y - H y$ $-Gy-Hy$	$G y - G y$ $Gy-Gy$ cancels out

Factor out

x

$x$ and

y

$y$

$G x - H x$ $Gx-Hx$	$=$ $=$	$- G y - H y$ $-Gy-Hy$
$x (G - H)$ $x(G-H)$	$=$ $=$	$y (- G - H)$ $y(-G-H)$
$x (G - H)$ $x(G-H)$	$=$ $=$	$- y (G + H)$ $-y(G+H)$

Finally, divide both sides by $G - H$ $G-H$

$x (G - H)$ $x(G-H)$	$=$ $=$	$- y (G + H)$ $-y(G+H)$
$x (G - H)$ $x(G-H)$ $\div (G - H)$ $-:(G-H)$	$=$ $=$	$- y (G + H)$ $-y(G+H)$ $\div (G - H)$ $-:(G-H)$

$x$ $x$	$=$ $=$	$\frac{- y (G + H)}{G - H}$ $(-y(G+H))/(G-H)$	$(G - H) \div (G - H)$ $(G-H)-:(G-H)$ cancels out

$x$ $x$	$=$ $=$	$\frac{y (G + H)}{H - G}$ $(y(G+H))/(H-G)$	Multiply $- 1$ $-1$ to the numerator and denominator

x = \frac{y (G + H)}{H - G}

$x=(y(G+H))/(H-G)$

Question 3 of 5

3. Question
Write $x$ $x$ as the subject of the equation below

$\frac{1}{z} = \frac{1}{y} + \frac{1}{x}$ $1/z=1/y+1/x$
- 1. $x = \frac{z + y}{y - z}$ $x=(z+y)/(y-z)$
- 2. $x = \frac{z y}{y - z}$ $x=(zy)/(y-z)$
- 3. $x = \frac{z - y}{y z}$ $x=(z-y)/(yz)$
- 4. $x = \frac{1}{y - z}$ $x=1/(y-z)$
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equation

Subtract $\frac{1}{y}$ $1/y$ from both sides

$\frac{1}{z}$ $1/z$ $=$ $=$ $1/y+1/x$

$1/z$ $-1/y$ $=$ $1/y+1/x$ $-1/y$

$1/z-1/y$ $=$ $1/x$ $1/y-1/y$ cancels out

$(y-z)/(zy)$ $=$ $1/x$

Cross multiply

$(y-z)/(zy)$ $=$ $1/x$

$x(y-z)$ $=$ $zy$

Finally, divide both sides by $y-z$

$x(y-z)$ $=$ $zy$

$x(y-z)$ $-:(y-z)$ $=$ $zy$ $-:(y-z)$

$x$ $=$ $(zy)/(y-z)$ $(y-z)-:(y-z)$ cancels out

$x=(zy)/(y-z)$

Question 4 of 5

4. Question

Solve for

$t$ given that

$v=20$ ,

$u=8$ and

$a=2$

$v=u+at$

$t=$ (6)

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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equation

Substitute the given values to solve for

$t$

$v$	$=$	$20$
$u$	$=$	$8$
$a$	$=$	$2$

$v$	$=$	$u+at$
$20$	$=$	$8+2t$	Substitute known values
$20$ $-8$	$=$	$8+2t$ $-8$	Subtract $8$ from both sides
$12$	$=$	$2t$	$8-8$ cancels out
$12$ $-:2$	$=$	$2t$ $-:2$	Divide both sides by $2$
$6$	$=$	$t$	$2-:2$ cancels out
$t$	$=$	$6$	Interchange the sides

$t=6$

Question 5 of 5

5. Question
Solve for $r$ given that $a=2$ and $S=25$

$S=a/(1-r)$

Write fractions in the format “a/b”
- $r=$ (23/25)
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equation

Multiply both sides of the equation to $1-r$

$S$ $=$ $a/(1-r)$

$S$ $xx(1-r)$ $=$ $a/(1-r)$ $xx(1-r)$

$S(1-r)$ $=$ $a$ $1/(1-r)xx(1-r)$ cancels out

Divide both sides of the equation to $S$

$S(1-r)$ $=$ $a$

$S(1-r)$ $-:S$ $=$ $a$ $-:S$

$1-r$ $=$ $a/S$

Leave only $r$ terms on the left

$1-r$ $=$ $a/S$

$1-r$ $-1$ $=$ $a/S$ $-1$ Subtract $1$ from both sides

$-r$ $=$ $a/S-1$ $1-1$ cancels out

Next, multiply both sides by $-1$

$-r$ $=$ $a/S-1$

$-r$ $xx(-1)$ $=$ $(a/S-1)$ $xx(-1)$

$r$ $=$ $1-a/S$

Finally, substitute the given values to solve for $r$

$a$ $=$ $2$

$S$ $=$ $25$

$r$ $=$ $1-a/S$

$r$ $=$ $1-2/25$ Substitute known values

$r$ $=$ $25/25-2/25$ Convert the whole number to a fraction

$r$ $=$ $23/25$

$r=23/25$

Quizzes

One Step Equations – Add and Subtract 1
One Step Equations – Add and Subtract 2
One Step Equations – Add and Subtract 3
One Step Equations – Add and Subtract 4
One Step Equations – Multiply and Divide 1
One Step Equations – Multiply and Divide 2
One Step Equations – Multiply and Divide 3
One Step Equations – Multiply and Divide 4
Two Step Equations 1
Two Step Equations 2
Two Step Equations 3
Two Step Equations 4
Multi-Step Equations 1
Multi-Step Equations 2
Solve Equations using the Distributive Property 1
Solve Equations using the Distributive Property 2
Solve Equations using the Distributive Property 3
Equations with Variables on Both Sides 1
Equations with Variables on Both Sides 2
Equations with Variables on Both Sides 3
Equations with Variables on Both Sides (Fractions) 1
Equations with Variables on Both Sides (Fractions) 2
Solve Equations with Variables on Both Sides using the Distributive Property 1
Solve Equations with Variables on Both Sides using the Distributive Property 2
Solve Equations with Variables on Both Sides using the Distributive Property 3
Solve Equations with Variables on Both Sides using the Distributive Property 4
Equation Word Problems 1
Equation Word Problems 2
Equation Word Problems 3
Equation Word Problems 4
Equation Word Problems (Age)
Equation Word Problems (Money)
Equation Word Problems (Harder)
Equation Problems with Substitution
Equation Problems (Geometry) 1
Equation Problems (Geometry) 2
Equation Problems (Perimeter)
Equation Problems (Area)
Change the Subject of an Equation 1
Change the Subject of an Equation 2
Change the Subject of an Equation 3

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