Question

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.

$22\left(3m-4\right)=8\left(2m+9\right)$

Short answer

The equation is a conditional equation and the solution of this equation is$m=\frac{16}{5}$.

Step-by-step solution

Step 1. Given information.

The given equation is$22\left(3m-4\right)=8\left(2m+9\right)$.

Step 2. Apply the distributive property to simplify the equation.

$$\begin{gathered} 22\times 3m-22\times 4=8\times 2m+8\times 9 \\ 66m-88=16m+72 \end{gathered}$$

Step 3. Collect all variables terms on another side of the equation.

Subtract $16m$from each side.

$$\begin{gathered} 66m-88-16m=16m+72-16m \\ 50m-88=72 \end{gathered}$$

Step 4. Collect all constant terms on another side of the equation and then simplify.

Add $88$to each side.

role="math" localid="1644044469809" $$\begin{gathered} 50m-88+88=72+88 \\ 50m=160 \end{gathered}$$

Divide each side by $50$.

$$\begin{gathered} \frac{50m}{50}=\frac{160}{50} \\ m=\frac{16}{5} \end{gathered}$$

From the above result, we can say that the given equation is true only for $m=\frac{16}{5}$.

So, the equation is a conditional equation.

Hence, the solution of the given equation is$m=\frac{16}{5}$.