Lial - College Algebra 13th Edition

Ch. 1 - Equations and Inequalities

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Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 78

The temperatures on the surface of Mars in degrees Celsius approximately satisfy the inequality $∣ C + 84 ∣ \leq 6$ . What range of temperatures corresponds to this inequality?

Problem 78

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. 4/(x+1)<2/(x+3)

Problem 79

For each equation, (a) solve for x in terms of y.. See Example 8. 4x^2 - 2xy + 3y^2 = 2

Problem 79

Solve each equation. See Example 7. (x-3)^2/5 = 4

Problem 79

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x+3)/(2x-5)≤1

Problem 79

Solve each equation. x/x+2 + 1/x+3 = 2/x²+2x

Problem 79a

Find each quotient. Write answers in standard form. -5 / i

Problem 79b

For each equation, (b) solve for y in terms of x. See Example 8.

$4 x^{2} - 2 x y + 3 y^{2} = 2$

Problem 80

Solve each rational inequality. Give the solution set in interval notation. See Examples 8 and 9. (x+2)/(2x+3)≤5

Problem 80

Solve each equation. 2/x+2 + 1/x+4 = 4/x²+6x+8

Problem 81

For each equation, (a) solve for x in terms of y. See Example 8. 2x^2 + 4xy - 3y^2 = 2

Problem 81

Solve each equation. (2x+3)^2/3 + (2x+3)^1/3 - 6 = 0

Problem 81a

Find each quotient. Write answers in standard form. 8 / -i

Problem 81b

For each equation, (b) solve for y in terms of x. See Example 8.

$2 x^{2} + 4 x y - 3 y^{2} = 2$

Problem 82

Solve each rational inequality. Give the solution set in interval notation.

$\frac{(9 x - 8)}{(4 x^{2} + 25)} < 0$

Problem 82

Solve each equation. See Example 7. (3x+7)^1/3-(4x+2)^1/3=0

Problem 83

To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x^2 - x | = 6, work Exercises 83–86 in order. For x^2 - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)

Problem 83

Solve each equation. See Example 7. (2x-1)^2/3 = x^1/3

Problem 83

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. x^2 - 8x + 16 = 0

Problem 83a

Find each quotient. Write answers in standard form. 2 / 3i

Problem 84

Solve each inequality. Give the solution set using interval notation.

$11 x \geq 2 (x - 4)$

Problem 84

Solve each equation. See Example 7.(x-3)^2/5=(4x)^1/5

Problem 85

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

Problem 85

Solve each equation. See Example 7. x^2/3 = 2x^1/3

Problem 85

Problem 86

Solve each inequality. Give the solution set using interval notation.

$7 x - 2 (x - 3) \leq 5 (2 - x)$

Problem 86

Solve each equation. See Example 7. 3x^3/4= x^1/2

Problem 87

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | 3x^2 + x | = 14

Problem 87

Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7

Problem 87

Solve each equation. See Examples 8 and 9. 2x⁴-7x²+5=0