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Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side

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Example

Find the solution of 2x – 3 = 7.
Add 3 to both sides.
2x – 3 + 3 = 7 + 3
2x = 10
Divide both sides by 2.
`((2x)/2) = 10/2`
x = 5.

Example

Solve 2y + 9 = 4
Transposing 9 to RHS
2y = 4 – 9
2y = – 5
Dividing both sides by 2,
y = `(- 5)/2`.
 
To check the answer:
LHS = `2((-5)/2) + 9 = - 5 + 9 = 4 = "RHS"`         ....(As required)

Example

Solve: `x/3 + 5/2 = - 3/2`.

Transposing `5/2` to the RHS, we get

`x/3 = (-3)/2 - 5/2 = - 8/2`

or `x/3 = - 4`

Multiply both sides by 3,

x = - 4 × 3

or x = - 12

Check: LHS = `- 12/3 + 5/2 = - 4 + 5/2 = (- 8 + 5)/2 = (- 3)/2` = RHS.

Example

Solve: `15/4 - 7x = 9`.

We have,

`15/4 - 7x = 9`

or - 7x = 9 - `15/4         ......("transposing" 15/4 "to RHS")`

or - 7x = `21/4`

or  `x = 21/(4 xx (-7))`    ......(Dividing both sides by - 7)  

or `x = - (3 xx 7)/(4 xx 7)`

or `x = - 3/4`

Check: LHS = `15/4 - 7((-3)/4) = 15/4 + 21/4 = 36/4` = 9 = RHS

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Shaalaa.com | Problems on Linear Equations in One Variable - Part 1

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Problems on Linear Equations in One Variable - Part 1 [00:12:20]
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Series: Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
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