Question

which of the following best describes the solution to the equation below?
14x + 9 = 7x + 37
a. exactly one real solution, x = 4
b. infinite real solutions
c. no real solutions

Explanation:

Step1: Subtract 7x from both sides

To solve the linear equation \(14x + 9 = 7x + 37\), we first aim to get all the \(x\)-terms on one side. Subtract \(7x\) from both sides of the equation:

\(14x - 7x + 9 = 7x - 7x + 37\)

Simplifying both sides, we have:

\(7x + 9 = 37\)

Step2: Subtract 9 from both sides

Next, we want to isolate the term with \(x\). Subtract 9 from both sides:

\(7x + 9 - 9 = 37 - 9\)

Simplifying both sides gives:

\(7x = 28\)

Step3: Divide by 7

To solve for \(x\), divide both sides of the equation by 7:

\(\frac{7x}{7} = \frac{28}{7}\)

Simplifying, we find:

\(x = 4\)

Since we obtained a single value for \(x\) (specifically \(x = 4\)), the equation has exactly one real solution.

Answer:

A. exactly one real solution, \(x = 4\)