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Problem 42
Explain why the equation | x | = √x² has infinitely many solutions.
Problem 43
Solve each equation or inequality. |4x + 3| - 2 = -1
Problem 44
Solve each equation or inequality. |8 - 3x| - 3 = -2
Problem 45
Solve each equation or inequality. |6 - 2x | + 1 = 3
Problem 46
Solve each equation or inequality. | 4 - 4x | + 2 = 4
Problem 47
Solve each equation or inequality. | 3x + 1 | - 1 < 2
Problem 48
Solve each equation or inequality. | 5x + 2 | - 2 < 3
Problem 49
Solve each equation or inequality. | 5x + 1/2 | -2 < 5
Problem 50
Solve each equation or inequality. | 2x+ 1/3 | +1 < 4
Problem 51
Solve each equation or inequality. | 10 - 4x | + 1 ≥ 5
Problem 52
Solve each equation or inequality. | 12- 6x | + 3 ≥ 9
Problem 53
Solve each equation or inequality. | 3x- 7 | + 1 > -2
Problem 55
Solve each equation or inequality. | 10- 4x | ≥ -4
Problem 57
Solve each equation or inequality. | 6- 3x | < -11
Problem 59
Solve each equation or inequality. | 8x + 5| = 0
Problem 60
Solve each equation or inequality. | 7 + 2x| = 0
Problem 61
Solve each equation or inequality. | 4.3x + 9.8| < 0
Problem 67
Write an equation involving absolute value that says the distance between p and q is 2 units.
Problem 73
Write each statement using an absolute value equation or inequality. r is no less than 1 unit from 29.
Problem 83
To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x2 - x | = 6, work Exercises 83–86 in order. For x2 - 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 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.) | 3x2 + x | = 14
Problem 89
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.) | 3x2 - 14x | = 5
Problem 91
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.) | x2 + 5x + 5 | = 1
Problem 93
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.) | x2 - 9 | = x + 3
Problem 95
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.) | 4x2 - 23x - 6 | = 0
Problem 97
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.) | x2 + 1 | - | 2x | = 0
Problem 1
Solve each equation. 2x+8 = 3x+2
Problem 3
Solve each equation. 5x-2(x+4)=3(2x+1)
Problem 5
Solve each equation. A= 24f / B(p+1), for f (approximate annual interest rate)
Problem 7
Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.)
A. 5x+3 =11
B.12x+6 =-4
C.100x =50(x+3)
D. 6(x+4) =x+24