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Equations & Inequalities: The Final C hallenge

Equations & Inequalities: The Final C hallenge. Equations. Ex. 1) 3(2x + 5) = -9. 1. Distribution . 6 x + 15 = -9. 2. Subtract 15 from both sides. – 15 – 15 . 6x = -24. 3. Divide both sides by 6. . 6 6. x = -4.

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Equations & Inequalities: The Final C hallenge

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  1. Equations & Inequalities: The Final Challenge

  2. Equations Ex. 1) 3(2x + 5) = -9 1. Distribution 6x + 15 = -9 2. Subtract 15 from both sides. – 15 – 15 6x = -24 3. Divide both sides by 6. 6 6 x = -4

  3. The goal is to get 1x alone. To do this, multiply both sides by , which is the reciprocal of . Ex. 2) 4 1 Reduce fractions if possible. Multiply fractions, and simplify.

  4. Subtract 5 from both sides to get the x term alone. Ex. 3) Multiply both sides by , which is the reciprocal of . Reduce fractions if possible. Multiply fractions, and simplify.

  5. To eliminate the fraction, multiply both sides by , which is the reciprocal of . Ex. 4) -3 1 Reduce fractions if possible. Add 4 to both sides to get 1x alone.

  6. Ex. 5) The perimeter of Mr. Mac Gregor’s garden is 64 meters. The length of the garden in 20 meters. What is the width of the garden? Write and solve an equation to answer this question! The perimeter is the distance around the outside of the rectangle. Let w = width of the rectangle 20 m P = 2(Length) + 2(width) P = 2L + 2w w w 64 = 2(20) + 2w 64 = 40 + 2w 20 m - 40 -40 24 = 2w 2 2 The width of the garden is 12 meters. 12 m = w

  7. Ex. 6) Students at the rec center are taking a trip to the county fair. The cost of the trip is $52 per student. This price includes a concert ticket worth $11 and 2 passes for the rides and the game booths. If the passes are worth the same amount of money, how much does 1 pass cost? Write and solve an equation to answer this question! Let x = cost of 1 pass Total cost = cost of concert ticket + cost of 2 passes 52 = 11 + 2x - 11 -11 41 = 2x 2 2 One pass would cost $20.50. $20.50 = x

  8. Inequalities Subtract 5 from both sides to get the x term alone. Ex. 7) 15 ≥ -2x + 5 -5 -5 10 ≥ -2x -2 -2 -5 ≤ x x ≥ -5 Divide both sides by -2. Reverse the direction of the inequality symbol because you divided by a negative number. Graph your answer on a number line. -7 -6 -5 -4 -3

  9. Ex. 8) A rental car company charges $45 plus $0.20 per mile to rent a car. Cindy wants to spend less than $100 for her car rental. How many miles she can drive and keep the bill under $100? Let x = the amount of miles driven 45 + 0.20x < 100 -45 -45 0.20x < 55 0.20 0.20 x < 275 Cindy must drive less than 275 miles.

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