Math Problem Statement
teach someone SOLVING LINEAR EQUATIONS
Solution
Solving Linear Equations: A Step-by-Step Guide
Linear equations are mathematical expressions that represent a straight line when graphed. They are of the form:
where:
- , , and are constants (numbers),
- is the variable we need to solve for.
Steps to Solve a Linear Equation
1. Simplify Both Sides
- If the equation has parentheses, distribute to eliminate them.
- Combine like terms on each side of the equation.
2. Isolate the Variable
-
To get the variable () on one side, we need to "undo" the operations around it by performing opposite operations (addition becomes subtraction, multiplication becomes division, etc.).
-
Start by adding or subtracting to move any constants ( or ) to the other side.
3. Solve for the Variable
- Once the variable term () is isolated, solve for by dividing by the coefficient of (which is ).
4. Check Your Solution
- Substitute the value of back into the original equation to verify that both sides are equal.
Example Problem
Solve the equation: .
Step 1: Simplify Both Sides
- The equation is already simplified.
Step 2: Isolate the Variable
- Subtract 5 from both sides:
Step 3: Solve for the Variable
- Divide both sides by 3:
Step 4: Check Your Solution
- Substitute back into the original equation:
Summary
- Simplify both sides of the equation.
- Isolate the variable by moving terms around.
- Solve for the variable.
- Check your solution.
Do you want more details on any of these steps, or do you have any questions?
Related Questions:
- How do you solve a linear equation with variables on both sides?
- What happens if a linear equation has no solution?
- How can you solve a linear equation with fractions?
- How do you solve a linear equation with decimals?
- What are the properties of equality used in solving equations?
Tip: Always perform the same operation on both sides of the equation to maintain the equality!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Linear equation formula ax + b = c
Theorems
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Suitable Grade Level
Grades 7-9