Linear Equations Numerical P1: Maths

A linear equation is a type of equation in which the highest power of the variable (usually x) is just 1. Linear equations form straight lines when plotted on a graph and have only one solution. In mathematics, the solution to an equation is the value that makes the equation true.

Solving a linear equation involves finding the variable's value that makes the equation true. The goal is to simplify the equation so that the variable is on one side of the equal sign and the constant is on the other side. This can be done using various algebraic techniques such as addition, subtraction, multiplication, and division.

Let's look at an example to illustrate this:
First, solve the equation 2x + 3 = 11.

We want to find the value of x that makes the equation true. We can start by subtracting 3 from both sides of the equation:
2x + 3 - 3 = 11 - 3

This simplifies to:
2x = 8

Next, we can isolate x by dividing both sides of the equation by 2:
\(\frac{2x}{2} = \frac{8}{2}\)

This simplifies to:
x = 4

Therefore, the solution to this equation 2x + 3 = 11 is x = 4.

Let's look at another example:
Solve the equation 3x + 4 = 13.