Question

Solve each equation. For each step. Identify the property used.

14 + 3n = 8n - 3(n-3)
22x + 11 = 4x - 7

(P.S. The properties that the problem is asking for are the properties of equality. Division property of equality, etc, etc.)

Answer 1

Solution of
`14 + 3n = 8n - 3(n-3)` => x = 5/2

Solution of
`22x + 11 = 4x - 7` => x=-1

Explanation:

We will solve the equations one by one

So,

`14 + 3n = 8n - 3(n-3)`

Applying Distributive property

`14 + 3n = 8n - 3n+9\\14+3n = 5n+9`

Subtraction property of equality (Subtracting 14 from both sides)

`14+3n-14 = 5n+9-14\\3n = 5n-5`

Subtraction property of equality (Subtracting 5n from both sides)

`3n-5n = 5n-5-5n\\-2n = -5`

Division property of equality (Dividing both sides by -2)

`(-2n)/(-2) = (-5)/(-2)\\n = (5)/(2)`

Second Equation:

`22x + 11 = 4x - 7`

Subtraction property of equality (Subtracting 11 from both sides)

`22x + 11-11 = 4x - 7-11\\22x = 4x-18`

Subtraction property of equality (Subtracting 4x from both sides)

`22x-4x = 4x-18-4x\\18x = -18`

Division property of equality (Dividing both sides by 18)

`(18x)/(18) = (-18)/(18)\\x = -1`

Hence

Solution of
`14 + 3n = 8n - 3(n-3)` => x = 5/2

Solution of
`22x + 11 = 4x - 7` => x=-1