This worksheet covers solving linear equations, writing expressions from word problems, and working with inequalities appropriate for 8th grade students.
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Expressions are like phrases that can be simplified (like '3x + 5') while equations are complete sentences with an equals sign that can be solved (like '3x + 5 = 14'). Have them identify whether they need to 'simplify and evaluate' (expression) or 'solve for the variable' (equation).
Negative answers and fractions are completely normal and often correct! Encourage them to always check their answer by substituting back into the original equation. If the equation balances, their solution is correct regardless of whether it's positive, negative, or a fraction.
Start by having them identify and define what the variable represents in one clear sentence. Then, break the word problem into smaller chunks, translating one phrase at a time. Practice with familiar contexts like age, money, or sports statistics before moving to abstract problems.
Multi-step equations are essential for algebra success, so don't skip them. Instead, break them down: first combine like terms, then isolate the variable term, then solve. Have them write out every step clearly and check their work by substituting their answer back into the original equation.
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The inequality symbol only flips when multiplying or dividing both sides by a negative number. Use concrete examples: if 5 > 3, then -5 < -3 (flipped). For practice, have them solve simple inequalities like -2x > 8 step by step, emphasizing this rule each time it applies.