Back
Problem 31
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1
Problem 31
An automobile repair shop charged a customer $1182, listing $357 for parts and the remainder for labor. If the cost of labor is $75 per hour, how many hours of labor did it take to repair the car?
Problem 31
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. -9x ≥ 36
Problem 31a
Simplify and write the result in standard form. √-108
Problem 32
Solve each equation in Exercises 15–34 by the square root property. (8x - 3)2 = 5
Problem 32
A repair bill on a sailboat came to $2356, including $826 for parts and the remainder for labor. If the cost of labor is $90 per hour, how many hours of labor did it take to repair the sailboat?
Problem 33
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)3/2 = 27
Problem 33
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 8x - 11 ≤ 3x - 13
Problem 33
In Exercises 29–36, simplify and write the result in standard form. √(32 - 4 × 2 × 5)
Problem 33
For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?
Problem 33a
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - x = x/10 - 5/2
Problem 34
A job pays an annual salary of $57,900, which includes a holiday bonus of $1500. If paychecks are issued twice a month, what is the gross amount for each paycheck?
Problem 34
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0
Problem 34a
Solve each equation in Exercises 15–34 by the square root property. (2x + 8)2 = 27
Problem 35
In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
Problem 35
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(x + 1) + 2 ≥ 3x + 6
Problem 35
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4
Problem 35
In Exercises 29–36, simplify and write the result in standard form. √(12 - 4 × 0.5 × 5)
Problem 36
Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? D = RT for R
Problem 37
In Exercises 37–52, perform the indicated operations and write the result in standard form. √-64 - √-25
Problem 37
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)2/3 = 16
Problem 37
In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = (1/2)bh for b
Problem 37
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 2x - 11 < - 3(x + 2)
Problem 37a
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x2 - 10x
Problem 38
Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? V = (1/3)Bh for B
Problem 38a
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8
Problem 39
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions.
Problem 39
In Exercises 37–52, perform the indicated operations and write the result in standard form. 5√-16 + 3√-81
Problem 39
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 - (x + 3) ≥ 4 - 2x
Problem 39
In Exercises 36–43, use the five-step strategy for solving word problems. An apartment complex has offered you a move-in special of 30% off the first month's rent. If you pay $945 for the first month, what should you expect to pay for the second month when you must pay full price?