Question

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

$15y+32=2\left(10y-7\right)-5y+46$

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$15y+32=2\left(10y-7\right)-5y+46$.

Step 2. Apply the distributive property.

Simplify the equation.

$$\begin{gathered} 15y+32=2\times 10y-2\times 7-5y+46 \\ 15y+32=20y-14-5y+46 \\ 15y+32=15y+32 \end{gathered}$$

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

Subtract $15y$from each side.

$$\begin{gathered} 15y+32-15y=15y+32-15y \\ 32=32 \end{gathered}$$

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".