Question

How do you solve for $ b $ in the formula $ 3a + 2b = c? $ ?

Answer 1

Hint: As we know that the above given equation $ 3a + 2b = c $ 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 answer:
As we know that the above given equation is a linear equation and to solve for $ b $ we need to isolate the term containing $ b $ on the left hand side i.e. to simplify $ 3a + 2b = c $ and solving for variable $ b $ , move all the terms containing $ a $ to the right.
Here we will get $ 2b = c - 3a $ and then by transferring the 4 from the variable $ y $ .
It gives,
 $ b = \dfrac{{c - 3a}}{2} $ .
Hence the answer of $ 3a + 2b = c $ for $ b $ is $ \dfrac{{c - 3a}}{2} $ .
So, the correct answer is “ $ \dfrac{{c - 3a}}{2} $ ”.

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.