Q39 - Geometry

Question

Find the value of the variable.

$7h+\left(90-h\right)=210$

Step-by-Step Solution

Answer

The value of the variable is $\mathit{h}\mathbf{=}\mathbf{20}$.

Step 1. Combine the like terms.

First remove all the brackets and combine the like terms 7h and h.

$\begin{array}{l}7h+\left(90-h\right)=210\\ 7h+90-h=210\\ 6h+90=210\end{array}$

Step 2. Subtract 90.

To find the value of variable h in the equation $6h+90=210$, subtract 90 from both sides of the equation.

$\begin{array}{l}6h+90-90=210-90\\ 6h=120\end{array}$

Step 3. Divide by 6.

Divide both sides of the equation $6h=120$ by 6 and cancel the common factors of 6 on both sides.

$\begin{array}{l}\frac{6h}{6}=\frac{120}{6}\\ h=\frac{20\times 6}{6}\\ h=20\end{array}$

Step 4. Verify the value.

In order to verify the value of h, substitute 20 for h into the equation $7h+\left(90-h\right)=210$.

$\begin{array}{l}7\times 20+\left(90-20\right)=210\\ 140+70=210\\ 210=210\text{ True}\end{array}$

Hence, the value of the variable is $h=20$.