Question

Solve the following linear equation for $p$.
$5p + 7 = 19 - 2p$

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 constant terms 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 $p$ we need to isolate the term containing $p$ on the left hand side i.e. to simplify $5p + 7 = 19 - 2p$ by keeping all the similar terms together.
Here we will get $5p + 2p = 19 - 7$ , we have moved the term containing similar variables to the left hand side of the equation and the constant terms to the right hand side of the equation.
On further solving by adding the terms we have , $7p = 12 \Rightarrow p = \ dfrac{{12}}{7}$.
Hence the answer of $5p + 7 = 19 - 2p$ for $p$ is $\ dfrac{{12}}{7}$ .

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.