Question

How do you solve for $h$ in $ - \dfrac{3}{7}h = 6$?

Answer 1

Hint: A linear equation is an equation for a straight line. The term which is involved in a linear equation is either a constant or a single variable or product of a constant. The two variables can never be multiplied. All linear equations have a line graph. Linear equations are the same as linear functions. The general form of writing a linear equation is $y = mx + c$ and $m$ is not equal to zero, where $m$ is the slope and $c$ is the point on which it cuts the y-axis.$y = mx + c$ is also known as equation of the line in slope-intercept form. This given question deals with a specific type of linear equation and that is, one step equations and inverse operations.

Complete step by step solution:
Given is $ - \dfrac{3}{7}h = 6$
We have to find the value of $h$ for which the left-hand side and right-hand side of the equation are equal.
In order to simplify for the value of $h$ in the given equation, we first have to take minus sign from left-hand side to right-hand side of the equation and we get,
$ \Rightarrow \dfrac{3}{7}h = - 6$
Next, we take$\dfrac{3}{7}$from left-hand side to right-hand side. On changing the side from left to right$\dfrac{3}{7}$ reciprocals itself.
$ \Rightarrow h = - 6 \times \dfrac{7}{3}$
After simplification we get,
$
\Rightarrow h = - 2 \times 7 \\
\Rightarrow h = - 14 \\
$
Hence, the value of $h$ is $ - 14$.

Note: Now that we know the value of $h$ is $ - 14$, there is a way to double check our answer. In order to double check the solution we are supposed to substitute the value of $h$ which we got as$ - 14$ in the given equation,$ - \dfrac{3}{7}h = 6$
$
\Rightarrow - \dfrac{3}{7}\left( { - 14} \right) = 6 \\
\Rightarrow - 3\left( { - 2} \right) = 6 \\
\Rightarrow 6 = 6 \\
$
Now, the left-hand side is equal to the right-hand side of the equation. So, we can conclude that our solution or the value of $h$ which we calculated was correct.