Question

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

$7v+42=11\left(3v+8\right)-2\left(13v-1\right)$

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$7v+42=11\left(3v+8\right)-2\left(13v-1\right)$.

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

$$\begin{gathered} 7v+42=11\times 3v+11\times 8-2\times 13v+2\times 1 \\ 7v+42=33v+88-26v+2 \end{gathered}$$

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

Subtract $7v$from each side.

$$\begin{gathered} 7v+42-7v=7v+90-7v \\ 42=90\left(false\right) \end{gathered}$$

This equation is false for all values of variable.

So, the equation is a contradiction.

Hence, the equation has no solution.