Question

Determine whether $\frac{2d+5}{3d+5}=\frac{2}{3}$ is sometimes, always, or never true. Explain.

Short answer

The statement is never true.

Step-by-step solution

Step 1. Given Information.

It is to be determined whether the given statement is sometimes, always,or never true.

$\frac{2d+5}{3d+5}=\frac{2}{3}$

Step 2. Explanation.

Simplifying the equation to solve for d:

$\begin{array}{l}\frac{2d+5}{3d+5}=\frac{2}{3}\\ 3\left(2d+5\right)=2\left(3d+5\right)\\ 6d+15=6d+10\\ 15=10\end{array}$

According to the statement d always cancels and 15 is never equal to 10.

Step 3. Conclusion.

Hence the statement is never true.