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Math 8 Unit 2 Equations Study Guide SOL 8.15 Name: ___________________________ Solve the inequalities and equations. Graph the inequalities. 1. x + 2 = –4x + 7 4. 7𝑦 − 4(3y – 5) > 80 7. 3 (2 − 7 3𝑦) = 6 10. 7x – 9 – 5x = 3 – (12 – 2x) 2. 3 4 𝑥 + 5 < 53 5. 3 + 5(𝑑 − 2) = –3d 5 3. −1.1𝑥 − 4 = 1.5 6. 4ℎ − 3 + 2 – h > 0 1 (6𝑥 3 8. – 2 (𝑤 − 1) = 20 9. 11. n – 2(n – 2) = –11 12. 4.1x – 1.3 = 0.7x + 25.9 + 3) = 2𝑥 − 5 Which property justifies the work between the steps? 13. 2 5 2 5 2 5 2 5 5 2 𝑥+5=9 Given 𝑥 + 5 + (–5) = 9 + (–5) Subtraction Property of Equality 𝑥 + 0 = 9 + (–5) ______________________ 𝑥=4 ______________________ ∙ 2 5 𝑥=4∙ 1𝑥 = 4 ∙ 𝑥=4∙ 5 Multiplication Property of Equality 2 5 ______________________ 2 5 ______________________ 2 𝑥 = 10 14. Simplify 7 + 4( −𝑛 + 3) = 43 Given 7 − 4𝑛 + 12 = 43 _____________________ −4𝑛 + 7 + 12 = 43 _____________________ – 4𝑛 + 19 = 43 Combine Like Terms – 4𝑛 + 19 – 19 = 43 − 19 Subtraction Property of Equality – 4𝑛 + 0 = 43 − 19 _____________________ −4𝑛 = 43 − 19 _____________________ −4𝑛 = 24 Simplify 1 1 (− 4) (– 4𝑛) = (− 4)24 1 1 Multiplication Property of Equality (− 4 ∙ −4) 𝑛 = (− 4)24 _____________________ 1𝑛 = −6 _____________________ 𝑛 = −6 _____________________ 15. You helped a friend move a short distance recently. The friend rented a truck for $15 an hour and rented a dolly for $5. Your friend paid a total of $80 for the rental. For how long did you rent the truck? 17. A boxing club charges nonmembers $14 per day for equipment rental. Members pay a yearly fee of $400 and a daily fee of $5 for equipment rental. Write and solve an equation to determine how many times members should use the gym to pay the same total cost as non-members. 16. A rental car agency charges $12 per day plus $.10 per mile to rent a certain car. Another agency charges $15 per day plus $.08 per mile to rent the same type of car. How many miles will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency? 18. Find the perimeter of the square. 19. Find the dimensions of the rectangle if the perimeter equals 50 ft. Define a variable, write an equation and solve it. 20. The product of a number and 3 is five less than a number. 21. Half of the sum of n and 3 is two more than a number. Write and solve the equation for the following models. 22. 23.