A linear equation is an equation of the first degree, meaning that the highest exponent of any variable is 1. Linear equations can be written in a variety of forms, but the most common form is:
ax + b = y
where a, b, and y are constants, and x is the variable.
A three-step linear equation is a linear equation that can be solved in three steps:
- Combine like terms on both sides of the equation.
- Isolate the variable on one side of the equation.
- Solve for the variable by dividing both sides of the equation by its coefficient.
How to Solve a Three-Step Linear Equation
Step 1: Combine like terms on both sides of the equation.
Like terms are terms that have the same variables raised to the same powers. For example, 2x and 3x are like terms, but 2x and x^2 are not like terms.
To combine like terms, simply add or subtract the coefficients of like terms. For example, the equation:
2x + 3x - 7 = x + 6
can be simplified by combining like terms on the left side of the equation:
5x - 7 = x + 6
Step 2: Isolate the variable on one side of the equation.
To isolate the variable, subtract any constant terms from the side of the equation that contains the variable. For example, the equation:
5x - 7 = x + 6
can be simplified by isolating the variable on the left side of the equation:
4x - 7 = 6
Step 3: Solve for the variable by dividing both sides of the equation by its coefficient.
The coefficient of the variable is the number that is multiplied by the variable. To solve for the variable, simply divide both sides of the equation by its coefficient. For example, the equation:
4x - 7 = 6
can be solved for the variable by dividing both sides of the equation by 4:
x = 3.5
Examples of Solving Three-Step Linear Equations
Example 1:
3x - 7 = x + 6
Solution:
Step 1: Combine like terms on both sides of the equation.
5x - 7 = x + 6
Step 2: Isolate the variable on one side of the equation.
4x - 7 = 6
Step 3: Solve for the variable by dividing both sides of the equation by its coefficient.
x = 3.5
Example 2:
2x + 5 = 3x - 8
Solution:
Step 1: Combine like terms on both sides of the equation.
-x + 5 = -8
Step 2: Isolate the variable on one side of the equation.
-x = -13
Step 3: Solve for the variable by dividing both sides of the equation by its coefficient.
x = 13
Example 3:
5x - 6 = 3x - 12
Solution:
Step 1: Combine like terms on both sides of the equation.
2x - 6 = -12
Step 2: Isolate the variable on one side of the equation.
2x = -6
Step 3: Solve for the variable by dividing both sides of the equation by its coefficient.
x = -3
Using a Three-Step Linear Equations Calculator
A three-step linear equations calculator is a tool that can be used to solve three-step linear equations. To use a three-step linear equations calculator, simply enter the equation into the calculator and press the “solve” button. The calculator will then display the solution to the equation.
Tips for Solving Three-Step Linear Equations
Here are some tips for solving three-step linear equations:
- Check your work by substituting the solution back into the original equation.
- If you get stuck, try breaking the equation down into smaller steps.
- Use a three-step linear equations calculator to verify your answer.
Conclusion
Three-step linear equations calculators are a valuable tool for solving the equations.
