Linear equations are one of the fundamental concepts in algebra. Whether you’re a student just starting to learn about equations or someone looking to refresh their knowledge, this comprehensive guide will walk you through the steps to solve linear equations. Let’s dive in!

What is a linear equation?

A linear equation is an algebraic equation that represents a straight line when graphed. It consists of variables raised to the power of 1 (i.e., first degree) and can be written in the form of “ax + b = 0,” where ‘a’ and ‘b’ are constants, and ‘x’ is the variable. Solving a linear equation involves finding the value of the variable ‘x’ that satisfies the equation.

What are the basic steps to solve a linear equation?

Here are the basic steps to solve a linear equation:

  • Step 1: Simplify both sides of the equation by combining like terms.
  • Step 2: Isolate the variable term on one side of the equation.
  • Step 3: Use inverse operations to eliminate any constants or coefficients attached to the variable.
  • Step 4: Solve for the variable by obtaining its value.
  • Step 5: Check the solution by substituting it back into the original equation.

Example

Let’s solve the following linear equation to illustrate the steps:

2x + 5 = 15

Step 1: Simplify both sides of the equation by combining like terms:

2x = 15 – 5

2x = 10

Step 2: Isolate the variable term:

x = 10/2

x = 5

Step 3: Use inverse operations:

x = 5

Step 4: Solve for the variable:

x = 5

Step 5: Check the solution:

2(5) + 5 = 15

10 + 5 = 15

15 = 15

This verifies that the solution, x = 5, is correct.

Additional Tips

  • Always perform the same operation on both sides of the equation to maintain its equality.
  • If you encounter fractions while solving, it helps to clear the fractions by multiplying both sides of the equation by the least common denominator.
  • If the variable cancels out during the solving process, the equation may be an identity (true for all values) or inconsistent (no solution).
  • Remember to always double-check your solution by substituting it back into the original equation. This ensures accuracy.

By following these steps and additional tips, you’ll be able to confidently solve linear equations in no time. Practice is key, so keep challenging yourself with various types of linear equations to master this essential skill!

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