Question

solve and check the linear equation. $\frac{x}{3}=\frac{16 - x}{5}$ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is { (type an integer or a simplified fraction.) } b. the solution set is {x| x is a real number}. c. the solution set is $varnothing$.

Explanation:

Step1: Cross - multiply the equation

Cross - multiplying $\frac{x}{3}=\frac{16 - x}{5}$ gives $5x = 3(16 - x)$.

Step2: Expand the right - hand side

Expanding $3(16 - x)$ gives $5x=48 - 3x$.

Step3: Add $3x$ to both sides

$5x+3x=48 - 3x+3x$, which simplifies to $8x = 48$.

Step4: Solve for $x$

Dividing both sides by 8, we get $x=\frac{48}{8}=6$.

Step5: Check the solution

Substitute $x = 6$ into the original equation. Left - hand side: $\frac{6}{3}=2$. Right - hand side: $\frac{16 - 6}{5}=\frac{10}{5}=2$. Since the left - hand side equals the right - hand side, $x = 6$ is the solution.

Answer:

A. The solution set is $\{6\}$