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Solve complex inequalities with variables on both sides, distribution, and combining like terms
Multi-step inequalities involve multiple operations and often include variables on both sides, requiring careful step-by-step solving with attention to the flip rule.
Move all variable terms to one side by adding or subtracting, then move constants to the other side. Finally, divide to isolate the variable, flipping the sign if dividing by a negative.
Apply the distributive property before moving terms around. For example, 2(x + 3) becomes 2x + 6. Then proceed with combining like terms and isolating the variable.
Yes, but it's conventional to have the variable on the left. Either way works as long as you properly track positive and negative coefficients.
If you get something like 5 < 5 (false), there's no solution. If you get 5 ≤ 5 (true), all real numbers are solutions.
Add or subtract coefficients of the same variable. For example, 5x + 2x = 7x. Keep constants separate from variable terms.
It's often easier to eliminate the smaller coefficient to keep numbers positive, but either approach works. Just be careful with negative coefficients and the flip rule.
Forgetting to flip the inequality sign when dividing by a negative number. Always check the sign of your final coefficient before dividing.
Yes! The solution can be any real number, including fractions and decimals. Your solution represents a range of values, not just integers.