Question

How do you solve $ 20 - \dfrac{k}{{15}} = 17? $

Answer 1

Hint: As we know that the above given equation $ a = p + prt $ is a linear equation. An equation for a straight line is called a linear equation. The standard form of linear equations in two variables is $ Ax + By = C $ . When an equation is given in this form it’s also pretty easy to find both intercepts $ (x,y) $ . By transferring the positive $ a $ to the right hand side value gives the required solution.

Complete step by step solution:
As we know that the above given equation is a linear equation and to solve for $ k $ we need to isolate the term containing $ k $ on the left hand side i.e. to simplify $ 20 - \dfrac{k}{{15}} = 17 $ and solving for variable $ k $ , move all the terms to the right.
Here we will transfer the $ + 20 $ to the right hand side and we get $ - \dfrac{k}{{15}} = 17 - 20 $ .
It gives us $ - \dfrac{k}{{15}} = - 3 $
Now since $ 15 $ is being divided in the left hand side, when we will transfer it to the right hand side it will turn into multiplication: $ - k = - 3 \times 15 $ . It can also be written as $ k = 45 $ , since the negative sign on both the sides will cancel each other.
Hence the required value of $ k $ is $ 45 $ .
So, the correct answer is “$ 45 $”.

Note: We should keep in mind the positive and negative signs while calculating the value of any variable as it will change it’s slope and value. In the equation $ Ax + By = C $ , $ A $ and $ B $ are real numbers and $ C $ is a constant, it can be equal to zero $ (0) $ also. These types of equations are of first order. Linear equations are also first-degree equations as it has the highest exponent of variables as $ 1 $ . The slope intercept form of a linear equation is $ y = mx + c $ ,where $ m $ is the slope of the line and $ b $ in the equation is the y-intercept and $ x $ and $ y $ are the coordinates of x-axis and y-axis , respectively.