Solving Equations

Equations are mathematical statements that show the equality of two expressions. Solving equations involves finding the value of the variable that makes the equation true. There are various methods to solve different types of equations, such as linear equations, quadratic equations, and more. Here, we will focus on solving linear equations.

Linear Equations

A linear equation is an equation of the form y = mx + b, where m and b are constants and x is the variable. To solve a linear equation, we need to isolate the variable x on one side of the equation.

Steps for Solving Linear Equations

1. Combine Like Terms: Simplify both sides of the equation by combining like terms.
2. Isolate the Variable: Use inverse operations (addition, subtraction, multiplication, division) to isolate the variable on one side of the equation.
3. Check Your Answer: Always check your solution by plugging it back into the original equation to ensure it satisfies the equation.

Example

Solve the equation: 3x - 5 = 7

Solution:

Step 1: Combine Like Terms

3x - 5 + 5 = 7 + 5

3x = 12

Step 2: Isolate the Variable

3x / 3 = 12 / 3

x = 4

Step 3: Check Your Answer

3(4) - 5 = 7

12 - 5 = 7

7 = 7 (True)

Therefore, the solution is x = 4.

Practice Problems

1. Solve the equation: 2x + 3 = 11

2. Solve the equation: 4(x - 2) = 20

3. Solve the equation: 5 + 2y = 3y - 1

Remember to always follow the steps for solving linear equations and check your answers to ensure accuracy!

Good luck with your practice!