Rearranging equations to find the value of unknown variable

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Question 1

Solve the following equations for $y$ . Enter your answers as fractions, such as 2/3, or integers but not decimals.

$\var{a}y + \var{d} = \var{b} +\var{c}y$

$y=\;$ interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\frac{ 15 }{ 2 }}$

In order to solve for the unknown variable, you must isolate the variable.
In the order of operation, multiplication and division are completed before addition and subtraction.

Example: 5 x - 6 = 3 x - 8

Subtract 3x from both sides of the equation: 2x - 6 = -8

Add 6 to both sides of the equation: 2x = -2 or x= -1

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Use the following steps in both parts to solve for unknown:

Part a)

1. Bring the terms of given variable to one side by changing signs.

Ex- $\var{a}y - \var{c}y$ = $\var{h}y$

2. Take all the constants to one side by changing signs

Ex- $\var{b}- \var{d}$ = $\var{w}$

3. Solving for y, we get-

$\ y$ = $\frac {\var{w}}{\var{h}}$

Part b)

1. Bring the terms of fractions of variables to one side by changing signs.

Ex- $\frac{\var{m}}{{y}} - \frac{\var{s}}{{y}} = \frac{\var{o}}{{y}}$

2. Take all the constants to one side by changing signs

Ex- $\var{t}- \var{n}$ = $\var{u}$

3. Solving for y, we get-

$\ y$ = $(\frac {\var{o}}{\var{u}})$

For futther help, check this video-

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