Unit 5 Summary

Pre-Algebra · Axiom Academy

SUMMARY Unit 5 Summary: Equations & Inequalities A recap of the key strategies for solving equations and inequalities — and turning real-world situations into them. Systematic approach: follow consistent steps and you can solve equations reliably every time. Inverse operations are fundamental: knowing how to undo an operation is the key to solving any equation. Watch for negatives: multiplying or dividing an inequality by a negative number means flipping the symbol. Verification matters: always check a solution by substituting it back into the original problem. Real-world power: equations and inequalities model countless situations — budgets, motion, mixtures, and more. Every equation is a balance. The whole method rests on keeping it balanced while you peel away operations in reverse to expose the variable. Balance property: whatever you do to one side, do to the other to keep equality. Inverse operations: undo with the opposite — add subtract, multiply divide. Order matters: undo in reverse PEMDAS — addition/subtraction first, then multiplication/division. Always check: substitute the solution back into the original equation to confirm it works. Core Concept Solving Equations From one inverse operation to several, the goal never changes: isolate the variable. Collect the variable terms on one side and the constants on the other, then finish. One-step: a single inverse operation — e.g. x + 5 = 12 , subtract 5 from both sides.

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