Question

Find the value of the variable.

$2\left(d+5\right)=3\left(d-2\right)$

Short answer

The value of the variable is $\mathit{d}\mathbf{=}\mathbf{16}$.

Step-by-step solution

Step 1. Apply the distributive property of multiplication.

The formula of distributive property of multiplication is given by: $x\left(y+z\right)=xy+xz$. Apply this property to the equation $2\left(d+5\right)=3\left(d-2\right)$.

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

Step 2. Subtract 2d.

To further simplify, subtract d from both sides of the equation $2d+10=3d-6$.

$\begin{array}{l}2d+10-2d=3d-6-2d\\ 10=d-6\end{array}$

Step 3. Add 6.

To find the value of variable d in the equation $10=d-6$, subtract 6 from both sides of the equation.

$\begin{array}{l}10+6=d-6+6\\ 16=d\end{array}$

Step 4. Verify the value.

In order to verify the value of d, substitute 16 for d into the equation $2\left(d+5\right)=3\left(d-2\right)$.

$\begin{array}{l}2\left(16+5\right)=3\left(16-2\right)\\ 2\left(21\right)=3\left(14\right)\\ 42=42\text{True}\end{array}$

Hence, the value of the variable is $d=16$.