Question

which of the following best describes the solution to the equation below?
$8x + 20 = -30 + 8x$
a. infinite real solutions
b. exactly one real solution, $x = -1\frac{7}{8}$
c. no real solutions

Explanation:

Step1: Subtract \(8x\) from both sides

Subtract \(8x\) from each side of the equation \(8x + 20=-30 + 8x\). We get \(8x - 8x+20=-30 + 8x - 8x\), which simplifies to \(20=-30\).

Step2: Analyze the result

The equation \(20 = - 30\) is a false statement. In linear equations of the form \(ax + b=cx + d\), if after simplifying (by getting all \(x\) terms on one side and constants on the other) we get a false statement (like a non - equal constant equation), then the original equation has no real solutions.

Answer:

C. no real solutions