Question

Is there a solution to 2(x-7)=2x-10

Answer 1

`\huge\text{Hey there!}`

`\large\text{ORIGINAL equation:}`

`\mathtt{2(x - 7) = 2x - 10}`

`\large\text{DISTRIBUTE 2 WITHIN the PARENTHESES:}`

`\mathtt{2(x) + 2(-7) = 2x - 10}`

`\mathtt{2x - 14 = 2x - 10}`

`\large\text{SUBTRACT 2x to BOTH SIDES of the equation:}`

`\mathtt{2x - 14 - 2x= 2x - 10 - 2x}`

`\large\text{SIMPLIFY IT!}`

`\mathtt{-14 = -10}`

`\large\text{ADD 14 to BOTH SIDES of the equation:}}`

`\mathtt{-14 + 14 =-10 + 14}`

`\large\text{SIMPLIFY IT!}`

`\mathtt{0 = 4}`

`\large\text{Thus this means that:}`

`\mathtt{You\ have\ NO\ solutions\ to\ this\ equation}`

`\huge\text{Therefore your answer should be:}`

`\huge\boxed{\mathtt{NO \ SOLUTION}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`

Answer 2

`\large\fbox{\textsf{No Solution.}}`

Explanation:

`\textsf{We are asked if there is a solution in the given equation.}`

`\textsf{Note that a solution is possible if both expressions \underline{actually} equal each other.}`

`\textsf{We should simplify the equation to find this out.}`

`\large\underline{\textsf{Solving;}}`

`\tt 2(x-7)=2x-10`

`\textsf{We can use the Distributive Property on the left side. 2 will multiply with the terms}`

`\textsf{inside the Parentheses.}`

`\tt (2 * x)+(2 * -7)=2x-10`

`\tt 2x-14 \\eq 2x-10`

`\textsf{Because the expressions don't equal each other, no solution is possible.}`

`\textsf{No matter what the value of x is, the equation will remain impossible.}`