Question

$\frac{2x}{x - 4} + \frac{2x - 5}{x - 3} = 8 \times \frac{1}{3}$
​

Answer 1

Step-by-step explanation:

To check to see if the value they've given me solves the equation, I'll plug the number, \frac{5}{2}

2

5

, in for the variable x in the equation. I'll then simplify, and make sure that the value on the left-hand side (LHS) of the equation is the same as the value on the right-hand side (RHS) of the equation.

Checking:

\small{ \textsf{LHS:}\, 2x = 2\left(\dfrac{5}{2}\right) }LHS:2x=2(

2

5

)

\small{ = \left(\dfrac{2}{1}\right) \left(\dfrac{5}{2}\right) }=(

1

2

)(

2

5

)

\small{ = \dfrac{5}{1} = 5 }=

1

5

=5

\small{ = \textsf{RHS} }=RHS

The left-hand side, after evaluating it at \frac{5}{2}

2

5

, came out to be the same value as the right-hand side. This means that the proposed solution value, x = \frac{5}{2}x=

2

5

, is indeed a valid solution to the equation.