Algebraic manipulation forms the foundation of solving math problems, including inequalities. This involves techniques to simplify and rearrange equations and inequalities to find the solution. For inequalities, you'll often:
- Combine like terms to simplify expressions
- Use addition or subtraction to isolate the variable
- Multiply or divide to solve for the variable
Consider the example we solved:
- First, we moved all \(x\) terms to one side: \(7x - 6 \leq 2x + 4\)
- We subtracted \(2x\) from both sides: \(5x - 6 \leq 4\)
- We then isolated the \(x\) term by adding 6: \(5x \leq 10\)
- Finally, we divided both sides by 5 to find \(x \leq 2\)
Mastering algebraic manipulation ensures you have the tools to simplify and solve complex inequalities effectively. It’s like untangling a knot step by step until you are left with a clear solution.