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

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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Problems on Linear Equations in One Variable - Part 1 [00:12:20]
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