Solving a linear type

Understanding the Concept of Solving a Linear Equation

Linear equations have only one variable, usually expressed as x or y, and no exponents on these variables.
The aim in solving these equations is to find the value of the unknown variable.
The standard form of a linear equation is Ax+B=0, where A and B are numbers and x is the unknown.
Linear equations are so named because their solutions, when plotted on a graph, fall on a straight line.

Steps to Solve a Linear Equation

Step 1: First, identify and simplify like terms on each side of the equality sign. ‘Like’ terms are those that share the same variable raised to the same power.
Step 2: Apply the principle of equivalence, which states that adding or subtracting the same number from both sides of an equation, or multiplying or dividing both sides of an equation by the same non-zero number, does not affect the solution to the equation.
Step 3: Use these operations of adding, subtracting, multiplying and dividing to isolate the variable on one side of the equation.

Example

Essential Tips

Always remember that what you do to one side of the equation, you must do to the other to maintain balance and equality.
Keep practising with linear equations of different complexities to build your proficiency.
If the equation involves fraction coefficients, consider multiplying across by denominators to clear the fractions.

In Summary

Solving linear equations involves identifying and simplifying like terms, applying the principle of equivalence and performing arithmetic operations to isolate the variable.
It’s a fundamental concept in algebra which provides the basis for solving more complex equations and algebraic expressions.