Question

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

$8(1-3x)+15(2x+7)=2(x+50)+4(x+3)+1$

Short answer

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

Step-by-step solution

Step 1. Given information.

The given equation is$8(1-3x)+15(2x+7)=2(x+50)+4(x+3)+1$.

Step 2. Use the Distributive Property to remove any parentheses. 

Combine like terms and simplify.

$$\begin{gathered} 8(1-3x)+15(2x+7)=2(x+50)+4(x+3)+1 \\ 8-24x+30x+105=2x+100+4x+12+1 \\ 6x+113=6x+113 \\ 6x-6x+113=6x-6x+113 \\ 113=113 \end{gathered}$$

This is a true statement.

Thus, the equation is an identity and the solution is all real numbers.

Step 4. Conclusion.

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