Questions: Solve and check the following equation. 5x - 7 = 8 + 4x What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation has a single solution. The solution set is 15 B. The solution set is x x is a real number. C. The solution set is ∅.

Solve and check the following equation. 5x - 7 = 8 + 4x What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation has a single solution. The solution set is 15 B. The solution set is x x is a real number. C. The solution set is ∅.
Transcript text: Solve and check the following equation. \[ 5 x-7=8+4 x \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation has a single solution. The solution set is $\{15\}$ B. The solution set is $\{x \mid x$ is a real number $\}$. C. The solution set is $\varnothing$.
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Solution

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Solution Steps

Step 1: Simplify the equation

Given the equation $5x - 7 = 4x + 8$, we move all terms involving $x$ to one side and constants to the other side to get $5x - 4x = 8 + 7$.

Step 2: Combine like terms

Combining like terms, we get $x(5 - 4) = 8 + 7$.

Step 3: Solve for $x$

Solving for $x$, we find $x = \frac{8 + 7}{5 - 4}$.

Final Answer:

The solution is $x = 15$.

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