Section 1.5: Solving Linear Equations
Solving a linear equation means finding the value of the variable that makes the equation true. The goal is to isolate the variable on one side of the equation using inverse operations.
Steps to Solve a Linear Equation:
- Simplify both sides (remove parentheses, combine like terms).
- Use addition/subtraction to move constants to one side.
- Use multiplication/division to isolate the variable.
- Check the solution by substituting it back into the original equation.
Example 1
Solve: \( 2x + 5 = 11 \).
\( 2x + 5 = 11 \)
Subtract 5 from both sides: \( 2x = 6 \)
Divide both sides by 2: \( x = 3 \).
Example 2
Solve: \( 4x - 7 = 9 \).
\( 4x - 7 = 9 \)
Add 7 to both sides: \( 4x = 16 \)
Divide both sides by 4: \( x = 4 \).
Practice Problems
- Solve: \( 3x + 4 = 10 \).
- Solve: \( 7x - 2 = 12 \).
- Solve: \( 5x = 20 \).
- Solve: \( \frac{x}{3} + 2 = 5 \).
- Solve: \( 9 - 2x = 1 \).