Page 506 - Algebra 1

*7. Find the common solution for the system of equations: -2y + 3x = 4.
(67)
- y + _3 x = 2 2
*8. Carpentry The shelf in a cabinet is set into a notch at a height of 12 inches. So (74) that the shelf can be adjusted to different heights, the cabinetmaker cuts notches
at one-inch intervals above and below the shelf. Write and solve an absolute-value equation for the maximum and minimum heights of a shelf set two notches above or below the 12-inch height.
*9. Write Why does the equation ⎢x - 6⎢ = 2x - 3 have no solution for x = -3? (74)
*10. Model Use a number line to diagram the solution of the absolute-value equation (74) ⎢x - 3 = 5. Then write the solution set to the absolute-value equation.
Measurement The diameter of a circular clamp is 10 centimeters. Its diameter can (74) be changed by changing its circumference.
a. If the circumference of the clamp is changed by ± 5cm, write an equation to find the clamp’s minimum and maximum diameters.
b. Solve the equation.
12. Graph the compound inequality x ≥ 5 OR x < 0.
(73)
13. Solve the inequality 6x < 12 OR 3x > 15. (73)
*14. Error Analysis Two students are solving ⎢z + 3⎢ = 5. Which student is correct? Explain (74) the error.
3 4 *11.
Student A
⎢z + 3⎢ = 5
⎢z⎢ + 3 = 5
⎢z⎢ = 5 - 3 = 2
z = 2 z = -2
The solution set is {2, -2}.
Student B
z + 3 = 5 z = 5 - 3 z = 2
z + 3 = -5 z = -5 - 3 z = -8
⎢z + 3⎢ = 5
The solution set is {2, -8}.
*15. Geometry The third side of a triangle must be greater than the difference of the (73) other two sides and less than the sum of the other two sides. Suppose that two
sides of a triangle have lengths 6 inches and 11 inches. Write a compound inequality that describes the possible values for the third side of the triangle.
16. Multi-Step Use the compound inequality 3x > 45 OR -2x ≥ 24. (73) a. Solve the compound inequality.
b. Graph the solution.
17. Factor the trinomial x2 - 3x - 40.
(72)
18. Landscaping To beautify a city park, landscapers use two sets of plans to lay out (72) rectangular flower beds. One set of plans for the area is described by the trinomial
x2 + 9x + 20. The other set is described by the trinomial x2 + 21x + 20. a. Determine the binomial factors of each set.
b. Which set can be used to lay out longer, narrower beds? Explain.
Lesson 74 491