Question

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

Answer 1

Answer:

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

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

Step-by-step 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)

$\frac{-2n}{-2} = \frac{-5}{-2}\\n = \frac{5}{2}$

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)

$\frac{18x}{18} = \frac{-18}{18}\\x = -1$

Hence

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

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