1) Tanya has a triangular garden bed in her back yard. The measure of the largest angle is 30° less than twice the measure of the smallest, and the measure of the middle angle is 10° more than the measure of the smallest angle. Find the measures of the three angles. Start your work by defining the unknown quantities in terms of a variable. Show all work and write a complete answer, including units.
2) Jacob decided to ride his bicycle across the country during his 3-month summer vacation. The route he took from Washington, DC to Portland, Oregon, covered a total of 3420 miles. To keep his mind occupied during some of the long flat stretches of countryside, he often did algebra problems in his head. One day, for example, he determined that his distance from his starting point was exactly 60 miles more than twice the distance remaining until the finishing point. How far was Jacob from the finishing point of his journey when he made that calculation? Start your work by defining the unknown quantities in terms of a variable. Show all work and write a complete answer, including units.
3) Solve the inequality. Write the answer using both set-builder notation and interval notation. Graph the solution set on a number line.
X - 3 > 7
4) Solve the inequality. Write the answer using both set-builder notation and interval notation. Graph the solution set on a number line.
2x - 4 < 7(x+3)
5) Solve the inequality. Write the answer using both set-builder notation and interval notation. Graph the solution set on a number line.
-2x - 6 ≥ 9x + 16
6) Solve the inequality. Write the answer using both set-builder notation and interval notation. Graph the solution set on a number line. Multiply both sides of the inequality by the LCD first to clear fractions.
-(4/5)x ≤ 2
7) Solve the inequality. Write the answer using both set-builder notation and interval notation. Graph the solution set on a number line. Multiply both sides of the inequality by the LCD first to clear fractions.
(1/2)x + (3/4) < (1/3)x + 1
8) Melissa is planning to invest a total of $17,000 in two accounts. If she invests $10,000 in a CD paying 12% annual simple interest, at what rate does the remainder of her money need to be invested so that the two investments together yield at least $1900 in yearly simple interest? (Set up and solve an inequality to answer this question).
9) Given the equation below, find four ordered pair solutions by completing the table, showing all work in the space below. Then use the ordered pairs to graph the equation. You may use the grid below or attach your own.
y = 3x + 2
10) Given the equation below, find four ordered pair solutions by completing the table, showing all work in the space below. Then use the ordered pairs to graph the equation. You may use the grid below or attach your own.
y = (4/5)x - 2
