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Best Wishes To: ___________________________________________ Date: _____________ Period: _______ HW 1 Solving Multi Step Equations and Inequalities 1. Solve the following equations. Determine if each of the following equations has one solution, no solutions, or infinitely many solutions. IF the equation has one solution, what is the solution? You MUST SHOW YOUR WORK!!! A) x – 3 = 4(x - 6) B) -5c – 9 + 2c = -1(3c + 9) # of solutions: _______________ Solution: ____________________ D) 3n + 1 – 2n = n – 2 # of solutions: _______________ Solution: ____________________ E) -4 = a + 6 – 5a # of solutions: _______________ Solution: ____________________ # of solutions: _______________ Solution: ____________________ # of solutions: _______________ Solution: ____________________ # of solutions: _______________ Solution: ____________________ C) 8 F) 2 4 q q 3 3 k 7 1 3 2. Solve the following Inequalities. Graph the solution to your inequality. You MUST SHOW YOUR WORK!!! A) 3x - 6 ≥ 27 B) 9 < 0 D) 2y + 2 – 9y ≥ 16 0 C) 8x 5 59 n -1 5 0 E) 4 4x 12 0 0 F) 28 3x 25 0 Best Wishes To: ___________________________________________ Write the inequality that best describes the graph. (3) ____________ 3. Date: _____________ 0 ______________ 4. (4) ______________ 5. (5) _______________ 6. (6) Period: _______ 3 0 0 0 5 8 11 Write an algebraic equation or inequality for each of the following situations. DO NOT SOLVE! 7. Your age, x, must be must be at least 16 years to 8. Seven less than twice a number is 21. drive on your own. 9) Keith has $100 in a savings account at the beginning of the summer. He wants to have at least $220 in the account at the end of the summer. He deposits $20 each week from his summer job. How many weeks does Keith need to work to meet his goal? ________________________________ _________________________ 10. Which is NOT a solution of the inequality: 14 – 2x ≥ 8 A -2 B 0 C 6 D -10 Best Wishes To: ___________________________________________ ANSWERS: 1) a. x = 7 d. no solution 2) a. x ≥ 11 d. y ≤ -2 Date: _____________ b. infinitely many solutions or All Real Numbers e. a = 5/2 f. k = -24 b. -50 > n c. x > 8 e. x ≥ -4 f. x ≥ 3/2 3) 0 < x ≤ 3 4) x ≥ 5 5) x > 8 6) x < 11 7) x ≥ 16 8) 2x – 7 = 21 9) 100 +20w ≥ 220; w ≥ 11, Keith will need to work at least 11 weeks. 10) C c. q = - 4 Period: _______