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mathematics
college algebra
College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. x² = 9
Specifications for a rod in an internal combustion engine call for a length of 5.375 inches. Lengths within 0.0025 inch of this length are acceptable. Express this situation as an inequality involving an absolute value. Use x as the actual rod length and solve for x.
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. P
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. 다 ≤ 16
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. x² < 1
Express the fact that x differs from 3 by less than 1/2 as an inequality involving an absolute value. Solve for x.
Express the fact that x differs from -4 by less than 1 as an inequality involving an absolute value. Solve for x.
Express the fact that x differs from -3 by more than 2 as an inequality involving an absolute value. Solve for x.
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. x² > 4
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. x² ≥ 1
Express the fact that x differs from 2 by more than 3 as an inequality involving an absolute value. Solve for x.
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. VI
In Problems 91–98, use the results found in Problems 89 and 90 to solve each inequality. 91 <
Elaine can complete a landscaping project in 2 hours with the help of either her husband Brian or both her two daughters. If Brian and one of his daughters work together, it would take them 4 hours to complete the project. Assuming the rate of work is constant for each person, and the two daughters
True or False Radical equations sometimes have extraneous solutions.
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. x ≥ −3 2 -3
In Problems 9–42, find the real solutions, if any, of each equation. V3x - 5 - Vx + 7 = 2
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. 4 ≤ x ≤ 6
In Problems 9–42, find the real solutions, if any, of each equation. V3(x+10) 4 = x -
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. -2
In Problems 9–42, find the real solutions, if any, of each equation. V1 x 3 = x + 2 -
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. -1 < x < 5
In Problems 9–42, find the real solutions, if any, of each equation. 2 V12 2x = x
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. 0≤x≤ 4
In Problems 9–42, find the real solutions, if any, of each equation. 3+√3x + 1 = x
In Problems 9–42, find the real solutions, if any, of each equation. x = 2√x - 1
In Problems 9–42, find the real solutions, if any, of each equation. √3x + x² = x - 2
In Problems 9–42, find the real solutions, if any, of each equation. x = 2√x - 1
In Problems 9–42, find the real solutions, if any, of each equation. √12 - x = x
In Problems 9–42, find the real solutions, if any, of each equation. √x²-x-4 = x + 2
In Problems 9–42, find the real solutions, if any, of each equation. V15 - 2x = x
In Problems 13–18, express the graph shown in blue using interval notation. Also express each as an inequality involving x. -1 0 1 2 3
In Problems 13–18, express the graph shown in blue using interval notation. Also express each as an inequality involving x. -1 0 1 2 3
In Problems 9–42, find the real solutions, if any, of each equation. √² + 16: 2 V5
In Problems 9–42, find the real solutions, if any, of each equation. x = 3√x
In Problems 13–18, express the graph shown in blue using interval notation. Also express each as an inequality involving x. -1 0 1 12 2 3
In Problems 9–42, find the real solutions, if any, of each equation. x = 8√x
In Problems 13–18, express the graph shown in blue using interval notation. Also express each as an inequality involving x. -2 -1 0 1 2
In Problems 9–42, find the real solutions, if any, of each equation. V12x3 = 0
In Problems 9–42, find the real solutions, if any, of each equation. x² + 2x = -1
In Problems 9–42, find the real solutions, if any, of each equation. V/1-2x 1 = 0
In Problems 13–18, express the graph shown in blue using interval notation. Also express each as an inequality involving x. -2 -1 0 1 2
In Problems 9–42, find the real solutions, if any, of each equation. V5t + 3 = -2
In Problems 13–18, express the graph shown in blue using interval notation. Also express each as an inequality involving x. -1 0 72 + 1 2 3
Which equation is likely to require squaring both sides more than once? (a) √x + 2 = √3x - 5 (c) √x + 1 + √x - 4 = 8 (b) x43x² = 10 (d) √3x + 1 = 5
In Problems 9–42, find the real solutions, if any, of each equation. V3t+ 4 = -6
In Problems 9–42, find the real solutions, if any, of each equation. V3t + 4 = 2
In Problems 41–58, fill in the blank to form a correct inequality statement. If x < 5, then x - 5_ 0.
In Problems 9–42, find the real solutions, if any, of each equation. x3/4 9x¹/4 ¹/4 = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. If x < −4, then x + 4 _____0.
In Problems 43–74, find the real solutions of each equation. x45x² + 4 = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. If x > −4, then x + 4 _____0.
In Problems 41–58, fill in the blank to form a correct inequality statement. If x= -4, then 3x - 12.
Which of the following will not change the direction, or sense, of an inequality? (a) Dividing both sides by a negative number (b) Interchanging sides (c) Taking the reciprocal of both sides (d) Subtracting a positive number from both sides
In Problems 41–58, fill in the blank to form a correct inequality statement. If x > 6, then x - 6_0.
If u is an expression that involves x, then the equation au2 + bu + c = 0, a ≠ 0, is called an equation ___________.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-9
In Problems 41–58, fill in the blank to form a correct inequality statement. If 8x 40, then x 5.
True or False The square of any real number is always nonnegative.
In Problems 41–58, fill in the blank to form a correct inequality statement. If x ≤ -4, then - 3x 12.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-25
True or False Factoring can only be used to solve quadratic equations or equations that are quadratic in form.
An apparent solution that does not satisfy the original equation is called a(n)_____ solution.(a) Extraneous (b) Radical (c) Imaginary (d) Conditional
In Problems 41–58, fill in the blank to form a correct inequality statement. If x ≥ 5, then - 4x -20.
The _____________ _____________ state that the sense, or direction, of an inequality remains the same if both sides are multiplied by a positive number, while the direction is reversed if both sides are multiplied by a negative number.
In Problems 43–74, find the real solutions of each equation. x4 - 10x2 + 25 = 0
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-64
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-12
In Problems 43–74, find the real solutions of each equation. 6x4 - 5x2 - 1 = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. If 3x12, then x 4.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi.2i4 (1 + i2)
In Problems 43–74, find the real solutions of each equation.(x + 2)2 + 7(x + 2) + 12 = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. 1 If x3, then x 2 -6.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-18
In Problems 43–74, find the real solutions of each equation.(2x + 5)2 - (2x + 5) - 6 = 0
In Problems 43–74, find the real solutions of each equation.(4x - 9)2 - 10(4x - 9) + 25 = 0
In Problems 43–74, find the real solutions of each equation.(2 - x)2 + (2 - x) - 20 = 0
In Problems 43–74, find the real solutions of each equation.2(s + 1)2 - 5(s + 1) = 3
In Problems 43–74, find the real solutions of each equation.3(1 - y)2 + 5(1 - y) + 2 = 0
In Problems 59–96, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3 – 5r < −7 -7
In Problems 59–96, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x-6
In Problems 43–74, find the real solutions of each equation. z¹/2 4z¹/4 + 4 = 0
In Problems 43–74, find the real solutions of each equation. x + √x = 6
In Problems 43–74, find the real solutions of each equation. t1/22t¹/4 + 1 = 0
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V(4 + 3i) (3i - 4)
In Problems 41–58, fill in the blank to form a correct inequality statement. If 0 < x≤ 10, then 0 < 1
In Problems 43–74, find the real solutions of each equation. 20 07 = x^ + x
In Problems 59–96, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x + 1 < 5
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. √(3 + 4i) (4i - 3)
In Problems 41–58, fill in the blank to form a correct inequality statement. If -5 < x < 0, then 1 1 < 0.
In Problems 43–74, find the real solutions of each equation. x + 8Vx = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. If x ≤ -4 < 0, then 1 1 < 0.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-45
In Problems 59–78, solve each equation in the complex number system.x2 - 4 = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. If 0 < 5 < x, then 0 1 1
In Problems 43–74, find the real solutions of each equation. - 4xVx = 0 0 = x
In Problems 59–78, solve each equation in the complex number system.x2 + 4 = 0
In Problems 41–58, fill in the blank to form a correct inequality statement. If 1 4 x > 1, then x -4.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-200
In Problems 43–74, find the real solutions of each equation. x1/2 3x¹/4 + 2 = 0
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