Algebra Skills Packet Key

Algebra 2 Trig Skills Review Packet Name * Key * Date Block Make sure you look at the reminders or examples before each set of problems to jog your memory! I. Solving Linear Equations 1. Eliminate parentheses \[5(2x-2)=4-2x+10\] \(10x-10=4-2x+10\rightarrow\) Eliminate parenthesis 2. Combine like terms \(10x-10=14-2x\) → Combine like terms 3. Eliminate terms by + or - +2x +2x 4. Isolate variable by or + \[12x-10=14\] \[\underline{+10+10}\] \[\frac{12x}{12}=\frac{24}{12}\] \[x=2\] → Eliminate terms by + or - → Isolate variable by ÷ Solve \[\frac{2}{3}x-1=x+7\] \[5x-2(3-x)=-(4-x)\] \[\frac{1}{3}x=8\] \[5x-6+2x=-4+x\] \[x=-24\] \[7x-6=-4+x\] \[6x=2\] \[x=\frac{1}{3}\] \[6(2x-1)+3=6(2-x)-1\] \[\frac{2}{3}x-2=\frac{3}{4}x+5\] \[12x-6+3=12-6x-1\] \[\frac{8}{12}x=\frac{9}{12}x+7\] \[12x-3=-6x+11\] \[\frac{-1}{12}x=7\] \[18x=14\] \[x=-84\] \[x=\frac{14}{18}\] \[x=\frac{7}{9}\] 5. A stockbroker earns a base salary of $40,000 plus 5% of the total value of the stocks, mutual funds, and other investments that the stockbroker sells. Last year, the stockbroker earned $71,750. What was the total value of the investments the stockbroker sold? II. Solving Inequalities Follow same procedure as in solving equations *EXCEPT in the last step. If you multiply or divide by a negative number, Be sure to reverse the direction of the inequality signs. Example 1: Example 2: [\frac{3x}{3} > \frac{-18}{3}] [\frac{-3x}{-3} > \frac{18}{-3}] [x > -6] [x < -6] Solve (-6 - x \ge -7x + 12) 7. [.5(2x-3) \ge -15 + 20x] [6x \ge 18] [10x - 15 \ge -15 + 20x] [x \ge 3] [-10x \ge 0] [x \le 0] You have $50 and are going to an amusement park. You spend $25 for the entrance fee and $15 for food. You want to play a game that costs $0.75. Write and solve an inequality to find the possible numbers of times you can play the game. If you play the game the 1 maximum number of times, will you have spent the entire $50? Explain.   \[50 - (25 + 15) = 10\] \[0.75x \le 10\] \[x \le \frac{40}{3} \text{ or } 13.\overline{3}\] can play 13 games and will have $0.25 left. III. Solving Absolute Value Equations and Inequalities 1. Isolate the Absolute Value \[2|x-6| + 3 \le 11\] \[2|x-6| \le 8\] \[|x-6| \le 4\] { Isolate the absolute value \(x-6 \le 4\) and \(x-6 \ge -4\) \(x \le 10\) and \(x \ge 2\) \[2 \le x \le 10\] Set up 2 inequalities Write your final answer as a compound inequality 2. Set up 2 equations/inequalities 3. Solve each equation/inequality 4. Write your final answer in {} or as a compound inequality.