Question

1. describe what is being done in each step while solving the equation.

a. $2(-3x + 4) = 5x + 2$
b. $-6x + 8 = 5x + 2$
c. $8 = 11x + 2$
d. $6 = 11x$
e. $x = \frac{6}{11}$

Explanation:

Step1: Apply distributive property

$2(3x + 4) = 5x + 2$ becomes $6x + 8 = 5x + 2$

Step2: Add $-5x$ to both sides

$6x + 8 - 5x = 5x + 2 - 5x$ simplifies to $8 = 11x + 2$

Step3: Subtract 2 from both sides

$8 - 2 = 11x + 2 - 2$ simplifies to $6 = 11x$

Step4: Divide by 11 on both sides

$\frac{6}{11} = \frac{11x}{11}$ simplifies to $x = \frac{6}{11}$

Answer:

a. Starting original equation: $2(3x + 4) = 5x + 2$
b. Applied distributive property to left side: $6x + 8 = 5x + 2$
c. Isolated $x$-terms to one side: $8 = 11x + 2$
d. Isolated the $x$-term: $6 = 11x$
e. Solved for $x$: $x = \frac{6}{11}$