Question

equation\
ewline $3(4x + 7) = 5(3x + 3)$\
ewline explanation\
ewline write the equation.\
ewline subtract $15x$ from each side.\
ewline reason\
ewline given\
ewline distributive property\
ewline subtraction property of equality\
ewline subtraction property of equality\
ewline division property of equality\
ewline $\boldsymbol{x = 2}$\
ewline $\boldsymbol{x = 6}$\
ewline $\boldsymbol{-3x = -6}$\
ewline $\boldsymbol{6x + 11 = 9}$\
ewline $\boldsymbol{-3x + 21 = 15}$\
ewline $\boldsymbol{12x + 21 = 15x + 15}$\
ewline $\boldsymbol{\text{multiply on each side}}$\
ewline $\boldsymbol{\text{divide each side by 4.}}$\
ewline $\boldsymbol{\text{divide each side by } -3.}$\
ewline $\boldsymbol{\text{subtract 11 from each side.}}$\
ewline $\boldsymbol{\text{subtract 21 from each side}}$

Explanation:

Step1: Write the given equation

$3(4x + 7) = 5(3x + 3)$

Step2: Apply distributive property

$12x + 21 = 15x + 15$

Step3: Subtract $15x$ from both sides

$12x - 15x + 21 = 15x - 15x + 15$
$-3x + 21 = 15$

Step4: Subtract 21 from both sides

$-3x + 21 - 21 = 15 - 21$
$-3x = -6$

Step5: Divide by $-3$ on both sides

$\frac{-3x}{-3} = \frac{-6}{-3}$
$x = 2$

Answer:

Equation	Explanation	Reason
$12x + 21 = 15x + 15$	Apply distributive property.	Distributive Property
$-3x + 21 = 15$	Subtract $15x$ from each side.	Subtraction Property of Equality
$-3x = -6$	Subtract 21 from each side.	Subtraction Property of Equality
$x = 2$	Divide each side by $-3$.	Division Property of Equality

Final solution: $x=2$