Question

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.

$60\left(2x-1\right)=15\left(8x+5\right)$

Short answer

The equation is a contradiction and the equation has no solution.

Step-by-step solution

Step 1. Given information.

The given equation is$60\left(2x-1\right)=15\left(8x+5\right)$.

Step 2. Apply the distributive property to simplify the equation.

$$\begin{gathered} 60\times 2x-60=15\times 8x+15\times 5 \\ 120x-60=120x+75 \end{gathered}$$

Step 3. Collect all variables terms on one side of the equation.

Subtract $120x$from each side.

$$\begin{gathered} 120x-60-120x=120x+75-120x \\ -60=75\left(false\right) \end{gathered}$$

This equation is false for all values of variable.

So, the equation is a contradiction.

Hence, the equation has no solution.