Question

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

$11\left(8c+5\right)-8c=2\left(40c+25\right)+5$

Short answer

The equation is an identity and the solution of this equation is "all real numbers".

Step-by-step solution

Step 1. Given information.

The given equation is $11\left(8c+5\right)-8c=2\left(40c+25\right)+5$

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

$$\begin{gathered} 11\times 8c+11\times 5-8c=2\times 40c+2\times 25+5 \\ 88c+55-8c=80c+50+5 \\ 80c+55=80c+55 \end{gathered}$$

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

Subtract $80c$from each side.

$$\begin{gathered} 80c+55-80c=80c+55-80c \\ 55=55 \end{gathered}$$

This is a true statement.

It means the equation is true for any value of the variable.

So, the equation is an identity.

Hence, the solution of this equation is "all real numbers".