Question

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

Answer 1

Never true

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\\eq-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 \\eq 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!}`

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`\frak{Amphitrite1040:)}`