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:

$\frac{1}{4}x-13=\frac{1}{4}(x+13)$

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:

$\begin{gathered} \frac{1}{4}x-13=\frac{1}{4}(x)+\frac{1}{4}(13) \\ \\ \frac{1}{4}x-13=\frac{1}{4}x+\frac{13}{4} \end{gathered}$

Multiply all terms by 4:

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

Subtract x from both sides:

$\begin{gathered} x-x-52=x-x+13 \\ \\ -52\ne13 \end{gathered}$

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