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Problem R.6.95
Solve each inequality. Give the solution set using interval notation. See Example 10. 10 ≤ 2x + 4 ≤ 16
Problem R.6.55
Solve each quadratic equation using the square root property. See Example 6. x² - 27 = 0
Problem R.6.50
Solve each quadratic equation using the zero-factor property. See Example 5.
9x² - 12x + 4 = 0
Problem R.6.45
Solve each quadratic equation using the zero-factor property. See Example 5. -4x² + x = -3
Problem R.6.93
Solve each inequality. Give the solution set using interval notation. See Example 10. -5 < 5 + 2x < 11
Problem R.6.49
Solve each quadratic equation using the zero-factor property. See Example 5. 4x² - 4x + 1 = 0
Problem R.6.67
Solve each quadratic equation using the quadratic formula. See Example 7.
x² - x - 1 = 0
Problem R.6.59
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 4x + 3 = 0
Problem R.6.75
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. 5x +2 ≤ -48
Problem R.6.65
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 6x = -7
Problem R.6.33
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 4(2x + 7) = 2x + 22 + 3(2x + 2)
Problem R.6.41
Solve each quadratic equation using the zero-factor property. See Example 5. x² - 5x + 6 = 0
Problem 8
CONCEPT PREVIEW Use choices A–D to answer each question.
A. 3x² - 17x - 6 = 0
B.(2x + 5)² = 7
C. x² + x = 12
D. (3x - 1) (x - 7) = 0
Which quadratic equation is set up for direct use of the square root property? Solve it.
Problem 11
Solve each linear equation. See Examples 1–3. 7x + 8 = 1
Problem 15
Solve each linear equation. See Examples 1–3. 7x - 5x + 15 = x + 8
Problem 19
Solve each linear equation. See Examples 1–3. 6(3x - 1) = 8 - (10x - 14)
Problem 23
Solve each linear equation. See Examples 1–3. 2 [x - (4 + 2x) + 3] = 2x + 2
Problem 25
Solve each linear equation. See Examples 1–3.
5/6x - 2x + 4/3 = 5/3
Problem 27
Solve each linear equation. See Examples 1–3.
(3x - 1)/4 + (x + 3)/6 = 3
Problem 29
Solve each linear equation. See Examples 1–3. 0.2x - 0.5 = 0.1x + 7
Problem 31
Solve each linear equation. See Examples 1–3. -4 (2x - 6) + 8x = 5x + 24 + x
Problem 2
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The point (4, ________) lies on the graph of the equation y = 3x - 6.
Problem 7
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The midpoint of the segment joining (0, 0) and (4, 4) is ________.
Problem R.7.1
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.
Problem 8
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The circle with equation x² + y² = 49 has center with coordinates ________ and radius equal to _______.
Problem 9
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.
Problem 11
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2. P(-5, -6), Q(7, -1)
Problem 13
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2.
P(8, 2), Q(3, 5)
Problem 15
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2.
P(-6, -5), Q(6, 10)
Problem 21
Concept Check Graph the points on a coordinate system and identify the quadrant or axis for each point. (3, 2)