Question

Is 3(x - 5) = 2(x - 5) + x always true or never true

Answer 1

Answer:

Never true

Step-by-step explanation:

Distribute on both sides to check

$3(x-5)\stackrel{?}{=}2(x-5)+x\\\\3x-15\stackrel{?}{=}2x-10+x\\\\3x-15\stackrel{?}{=}3x-10\\\\-15\stackrel{?}{=}-10\\\\-15\neq-10$

Therefore, since both sides aren't equal to each other, the answer is never true

Answer 2

$\huge\textbf{Hey there!}$

$\large\textbf{QUESTION: Is 3(x - 5) = 2(x - 5) + x always true or}\\\large\textbf{never true?}$

$\large\textsf{Equation \#1}$

$\large\textbf{3(x - 5)}\\\\\large\text{DISTRIBUTE 3 WITHIN the PARENTHESES}\\\\\large\textbf{= 3(x) + 3(-5)}\\\\\large\textbf{= 3x - 15}\\\\\large\textbf{Thus, your answer is: 3x - 15}\leftarrow\large\text{ we have to see if equation \#2}\\\large\text{gives you the same answer/result as equation \#1. }$

$\large\textsf{Equation \#2}$

$\large\textbf{2(x - 5) + x}\\\\\large\text{DISTRIBUTE 2 WITHIN the PARENTHESES}\\\\\large\textbf{= 2(x) + 2(-5) + x}\\\\\large\textbf{= 2x - 10 + x}\\\\\large\textbf{= 2x - 10 + 1x}\\\\\large\text{COMBINE the LIKE TERMS}\\\\\large\textbf{= 3x - 10}\\\\\large\textbf{Thus, your answer is: 3x - 10}\leftarrow\larget\text{from the looks of it equation}\\\large\text{\#2 \& equation \#1 are NOT equivalent to each other.}$

$\huge\boxed{\mathsf{3x - 15 \neq 3x - 10}}$

$\huge\textbf{Therefore, your answer is: \boxed{\mathsf{never \ true}}}\huge\checkmark$

$\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}$

~$\frak{Amphitrite1040:)}$