Question

which statement regarding the number of solutions for the linear equation shown below is true? 1/4 x - 13 equals 1/4 (x + 13)

Answer 1

Given the equation:

`(1)/(4)x-13=(1)/(4)(x+13)`

Let's find the number of solutions.

Apply the following conditions:

x = x.....................Infinitely many solutions

x ≠ y ......................No solution

x = 2........................One solution

Let's simplify the equation

Apply distributive property:

`\begin{gathered} (1)/(4)x-13=(1)/(4)(x)+(1)/(4)(13) \\ \\ (1)/(4)x-13=(1)/(4)x+(13)/(4) \end{gathered}`

Multiply all terms by 4:

`\begin{gathered} (1)/(4)x(4)-13(4)=(1)/(4)x(4)+(13)/(4)(4) \\ \\ x-52=x+13 \end{gathered}`

Subtract x from both sides:

`\begin{gathered} x-x-52=x-x+13 \\ \\ -52\\e13 \end{gathered}`

Since the right hand side does not equal the left hand side of the equation, we can say there is no solution.

ANSWER:

There is no solution