Question

How do you solve $5x - 4 = 2x - 13$?

Answer 1

Hint: To solve this sum, we need to first group the variables on one side and the constants on the other side. Once we have done the grouping and changed the signs accordingly, we simply solve the sum further by applying the necessary functions. We will then have our required answer.

Complete step-by-step solution:
In this question, we are asked to solve a linear equation.
This equation is said to be linear in nature as it contains variables only raised to the power of $1$.
The given equation is-
$ \Rightarrow 5x - 4 = 2x - 13$
Let us group the equation clearly first.
We keep the variables on the left hand side of the equal to symbol, while we keep the constants on the right hand side of the equal to symbol.
Thus, we have $5x - 2x = 4 - 13$
As we change the sides of the respective variables and constants, their signs also change.
Let us solve the equation further:
$ \Rightarrow 3x = - 9$
On dividing both the sides of the equation with $ + 3$, we get:
$ \Rightarrow x = - 3$

Thus, we have our required answer for the variable x as -3.

Note: These kinds of equations are known as Linear Equations. They are also known as the first order equation as they only have variables raised to the power of one. They are the simplest and the most elemental type of equations. These equations are generally defined for lines in a coordinate system. An equation for a straight line is called a linear equation. The equation for a straight line is given as: \[y = mx + c\] Where ‘m’ represents the slope or the angle formed by the line on the x-axis, and c represents the y-intercept.