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- 1Solve single variable linear inequalities with rational coefficients.
- 2Show the inequality 2x + 3 > 11 on the board; ask learners to identify which operations separate the variable from the numbers.
- 3Learners whisper to their partner one operation they would use to isolate x in the inequality 3x - 5 < 10.
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- SOLVING LINEAR INEQUALITIES USING INVERSE OPERATIONS
- 1Write 2x + 6 ≤ 18 on the board using the ruler and graph board; demonstrate subtracting 6 from both sides, then dividing by 2, speaking aloud each step with the textbook inequality rules.
- 2Learners use their exercise books to solve x/4 - 2 > 1 following the same inverse operation pattern; a volunteer writes the solution on the board.
- 3Learners solve 5x + 3 ≥ 28 in pairs using the calculator to check final answers.
- SOLVING INEQUALITIES WITH RATIONAL COEFFICIENTS
- 4Write 1.5x - 4 < 8 and (2/3)x + 5 ≥ 11 on the board; explain that rational coefficients mean decimals and fractions; solve both inequalities step-by-step using the textbook method.
- 5Learners solve (3/4)x - 2 ≤ 7 in their exercise books, showing all working; call on a learner who finished first to show their working on the board.
- 6Learners solve 2.5x + 1.2 > 9.2 using the calculator for decimal arithmetic; pairs compare answers.
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- 1Textbook
- 2Exercise book
- 3Calculator
- 4Ruler and graph board
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- 1A learner reads aloud one inequality solved today; the class repeats the solution steps chorally.
- 2Learners show fingers 1–5 to rate their confidence in solving inequalities with rational coefficients.
Exercise
- 1Solve the inequality (1/2)x + 4 < 10 and state your solution.
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- 1Illustrate solution sets of linear inequalities on the number line.
- 2Draw a number line from 0 to 10 on the board; ask: 'If x > 5, which numbers can x be?' and have learners call out examples.
- 3Show a number line with a filled circle at 3 and an arrow pointing right; learners discuss with a partner what inequality this represents.
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- REPRESENTING SOLUTIONS ON THE NUMBER LINE
- 1Solve x + 2 > 5 on the board using the textbook method, obtaining x > 3; draw a number line using the ruler and graph board, marking 3 with an open circle and shading to the right.
- 2Solve 2x - 4 ≤ 6 to get x ≤ 5; learners draw the number line in their exercise books, using a filled circle at 5 and shading left.
- 3Learners solve 3x + 1 < 10 in pairs, draw the solution on their number line, and compare with another pair's diagram.
- DISTINGUISHING OPEN AND CLOSED CIRCLES ON NUMBER LINES
- 4Write four inequalities on the board: x > 2, x ≥ 2, x < 7, x ≤ 7; using the ruler and graph board, draw number lines for each, labeling open circles for > and <, filled circles for ≥ and ≤.
- 5Learners sketch four number lines in their exercise books for the inequalities (1/2)x > 1, 2x ≤ 6, x + 3 > 4, and 3 - x ≥ 0; volunteers show their work for one inequality each.
- 6Learners match five inequalities to their correct number line representations displayed on the board.
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- 1Textbook
- 2Exercise book
- 3Ruler and graph board
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- 1Ask: 'If the circle is open, what symbol is the inequality using?' Learners respond chorally: 'Greater than or less than.'
- 2Learners write one inequality symbol that uses a closed circle in their exercise books and hold them up.
Exercise
- 1Solve x - 3 < 4 and draw its solution set on a number line using the ruler and graph board.
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- 1Solve real-life problems involving linear equations and inequalities.
- 2Present: 'Ama is buying kelewele at Makola Market for GH₵2.50 each; she has GH₵20. What is the maximum number she can buy?' Ask: 'Is this asking for an exact answer or a limit?'
- 3Learners pair-share one real situation from their community where they need to find how many items they can afford with limited money.
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- SETTING UP EQUATIONS AND INEQUALITIES FROM REAL-LIFE CONTEXTS
- 1A trotro charges GH₵3 per passenger; if a driver needs to collect at least GH₵60, write the inequality 3x ≥ 60 on the board where x is the number of passengers; solve to find x ≥ 20 using the textbook method.
- 2Learners read: 'A carpenter has 260 metres of wood for fencing a rectangular field 50 metres wide; find the length.' Set up the equation 2(x + 50) = 260 in the exercise book; solve x = 80 metres.
- 3Learners solve: 'A chop bar operator makes a profit of GH₵4 per plate of waakye; she needs GH₵200 profit. How many plates must she sell?' Set up 4x = 200, solve x = 50 plates.
- SOLVING AND INTERPRETING REAL-LIFE INEQUALITY PROBLEMS
- 4Present: 'A farmer has 300 yams to share equally among his workers; if each worker gets at least 15 yams, write the inequality 300 ÷ x ≥ 15 or x ≤ 20; this means at most 20 workers.' Solve using the textbook method.
- 5Learners solve: 'A school trip costs GH₵150 per learner; the budget is GH₵4500. Write and solve 150x ≤ 4500 to find the maximum number of learners.' Use the calculator for division; learners write answers in exercise books.
- 6Pairs solve: 'A seamstress earns GH₵8 per hour; she wants to earn more than GH₵80. Write and solve 8x > 80 for minimum working hours; discuss why x > 10 means she must work more than 10 hours.'
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- 1Textbook
- 2Exercise book
- 3Calculator
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- 1A learner presents one real-life problem solved today; the class identifies whether it was an equation or inequality.
- 2Learners thumbs-up if they can now solve a real-life problem that uses inequalities.
Exercise
- 1A trader sells fufu for GH₵2 per portion; she has GH₵50. Write and solve an inequality to find the maximum number of portions she can afford to buy.
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