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Algebra I - Equations & Proportions

Learn how to write and solve equations, solve one-step and multi-step equations, solve equations with variables on both sides, solve equations with grouping symbols, solve absolute value equations, and solve proportions. Also, understand percent of change and its applications.

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Algebra I - Equations & Proportions

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  1. Algebra I Chapter 2

  2. Section 2-1 Writing Equations Ex1) Translate each sentence into an equation. Pay attention to the words is, is as much as, is the same as, is identical to • Seven times a numbers squared is five times the difference of k and m • Fifteen times a number subtracted from 80 is 25

  3. Section 2-1 Ex2) Translate the sentence into a formula: the area of a triangle equals the product of ½ the length of the base and the height Ex3) Translate each equation into a sentence • 6z – 15 = 45 b)

  4. Section 2-2: Solving One-Step Equations Solution – Equivalent Equations –

  5. Section 2-2: Solving One-Step Equations Solution – the value(s) that make an equation true Equivalent Equations – equations that have the same solution

  6. Section 2-2 Ex1) Solve the one-step equations and check your answer! • x – 22 = 54 b) y + 63 = 79 c) 3m = -12 d) e) f) 5 = -6 + n

  7. Section 2-2 Ex2) Of a group of female students surveyed, 225 or about said they talk on the phone while they watch t.v. How many girls were surveyed?

  8. Section 2-2 Ex3) Solve • g + 5 = 33 b) 104 = y – 67 c) d)

  9. Section 2-3 Solving Multi-Step Equations Ex1) Solve • 11x – 4 = 29 b) c) 2a – 6 = 4 d)

  10. Section 2-3 Ex2) Sarah is buying a pair of water skis that are on sale for 2/3 of the original price. After he uses a $25 gift certificate, the total cost before taxes is $115. What was the original price of the skis? Write an equation and solve.

  11. Section 2-3 Consecutive Integers – integers in counting order

  12. Section 2-3 Ex3) Write an equation for the following problem, then solve the equation. Find 3 consecutive odd integers with a sum of -51

  13. Section 2-4: Solving Equations with Variables on Both Sides Steps for Solving Equations with Multiple Steps 1. 2. 3. 4. 5.

  14. Section 2-4: Solving Equations with Variables on Both Sides Steps for Solving Equations with Multiple Steps 1. Distribute (get rid of parenthesis) 2. Combine Like terms on the same side of = 3. Get variables together on one side of = 4. Add or subtract the number NOT attached to the variable 5. Multiply or divide the number that IS attached to the variable

  15. Section 2-4 Ex1) Solve • 2 + 5k = 3k – 6 b) 3w + 2 = 7w c) 5a + 2 = 6 – 7a d)

  16. Section 2-4: Equations with Grouping Symbols Ex2) a) b) 8s – 10 = 3(6 – 2s) c) 7(n – 1) = -2(3 + n)

  17. Section 2-4: Special Solutions Ex2) Solve • 5x + 5 = 3(5x – 4) – 10x b) 3(2b – 1) – 7 = 6b – 10

  18. Section 2-4 Find the value of x so that the figures have the same area 10cm x cm 6 cm 3cm x cm Find the value of x so that the figures have the same perimeter x 6 x 2x + 2

  19. Section 2-5: Solving Equations Involving Absolute Value Absolute Value – The distance a point is from zero on a number line Ex1) Evaluate a) if m = 4 b) if x = 2

  20. Section 2-5 Solve the absolute value equation Ex2) Steps • Split the equation into 2 equations, one that = the positive number and one that = the negative number • Solve each equation (you will have 2 answers!)

  21. Section 2-5 Ex3) Solve a) b) c) Ex4) Write an absolute value equation for the graph with points on 11 and 19 (draw a graph)

  22. Section 2-6: Ratios and Proportions Ratio – Proportion – Means-Extremes Property of Proportion

  23. Section 2-6: Ratios and Proportions Ratio – A comparison between two numbers using division (fraction) Proportion – two ratios that are equal Means-Extremes Property of Proportion

  24. Section 2-6 Ex1) Determine if the ratios are equivalent. Answer yes or no. a) b) c)

  25. Section 2-6 Ex2) Use cross-multiplication to solve the proportions a) b) c)

  26. Section 2-6 Ex3) The Ramsey Cascades Trail is about inches long on a map with a scale of 3 in = 10 miles. What is the actual length of the trail. Let l represent the length.

  27. Section 2-7 Percent of Change Percent of Change – Percent of Increase – Percent of Decrease –

  28. Section 2-7 Percent of Change Percent of Change – the ratio of the change in an amount to the original amount expressed as a percent Percent of Increase – when the new number is greater than the original number Percent of Decrease – when the new number is less than the original number

  29. Section 2-7 Ex1) Determine whether each percent of change is a percent increase or a percent decrease. Then find the percent of change. • Original: 20 b) Original: 25 Final: 23 Final: 17

  30. Section 2-7 Ex2) The total number of passengers on cruise ships increased 10% from 2007 to 2009, how many were there in 2007?

  31. Section 2-7 Ex3) Marta is purchasing wire and beads to make jewelry. Her merchandise is $28.62 before tax. If the tax is 7.25% of the total sales, what is the final cost? Ex4) Since Tyrell has earned good grades in school, he qualifies for the good student discount on his car insurance. His monthly payment without the discount is $85. If the discount is 20%, what will he pay each month?

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