Solving Equations
Solving Equations in Algebra
In algebra, solving equations involves finding the value of the unknown variable (usually denoted as \( x \)) that makes the equation true. The goal is to isolate \( x \) on one side of the equation. Here are the six basic types of equations and how to solve them:
- Addition Equation: \( x + a = b \) → \( x = b – a \).
- Subtraction Equation: \( x – a = b \) → \( x = b + a \).
- Multiplication Equation: \( a \cdot x = b \) → \( x = \frac{b}{a} \).
- Division Equation: \( \frac{x}{a} = b \) → \( x = b \cdot a \).
- Reciprocal Equation: \( \frac{a}{x} = b \) → \( x = \frac{a}{b} \).
- Combination Equation: Use inverse operations to isolate \( x \).
Exercises
Solve the following equations. Check your answers by clicking the “Check Answer” button.
1. Solve: \( x + 5 = 12 \)
2. Solve: \( x – 3 = 8 \)
3. Solve: \( 4x = 20 \)
4. Solve: \( \frac{x}{2} = 6 \)
5. Solve: \( \frac{7}{x} = 1 \)
6. Solve: \( x + 10 = 22 \)
7. Solve: \( x – 7 = 15 \)
8. Solve: \( 3x = 27 \)
9. Solve: \( \frac{x}{4} = 5 \)
10. Solve: \( \frac{10}{x} = 2 \)