1.2 Linear Equations and Rational Equations
Solve and state whether the equation is and identity, conditional, or inconsistent.
7(x - 4) = x + 2
x = 5; conditional equational
Perform the indicated operation and put in standard form.
4i(3i - 2)
-12 - 8i
Solve by factoring.
5x2 + 20x = 0
x = -4, 0
Solve the polynomial.
2x4 = 50x2
x = -5, 0, 5
Express in set builder notation and graph on a # line.[-3,5)
{x | -3 (less than or equal to) x < 5}
Solve and state whether the equation is and identity, conditional, or inconsistent.
2x/3 = x/6 + 1
x = 2; conditional equation
Perform the indicated operation and put in standard form.
(8 - 3i) - (17 - 7i)
-9 + 4i
Solve using the square root property.
2x2 - 3 = 125
x = -8, 8
Solve the radical equation.
(the square root of 2x-3) + x = 3
x = 2
Solve, write in interval notation and graph.
-6x + 3 (less than/equal to) 15
Solve and state whether the equation is and identity, conditional, or inconsistent.
7x + 13 = 2(2x - 5) + 3x + 23
infinitely many solutions; identity
Perform the indicated operation and put in standard form.
(3 - 4i)2
5 - 24i
Solve by completing the square.
x2 - 12x + 27 = 0
x = 3, 9
Solve the equation with rational exponents.
3x3/4 - 24 = 0
x = 16
Solve, write in interval notation and graph.
|2x+3| (less than/equal to) 15
[-9,6]
Solve and state whether the equation is an identity, conditional, or inconsistent.
7/(x-5) + 2 = (x+2)/(x-5)
no solution; inconsistent equation
Perform the indicated operation and put in standard form.
(Square root of -32) - (Square root of -18)
(square root of 2) i
Solve by using the quadratic formula.
x2 - 2x + 19 =0
x = 1 + 3i(square root of 2), 1 - 3i(square root of 2)
Solve by making an appropriate substitution.
x4 - 5x2 + 4 = 0
x = -2, -1, 1, 2
Solve, write in interval notation and graph.
5(x - 2) - 3(x + 4) (greater than/equal to) 2x - 20
empty set
Solve and state whether the equation is and identity, conditional, or inconsistent.
(x+2)/(x+3) + 1/(x2+2x-3) - 1 = 0
x = 2; conditional equation
Perform the indicated operation and put in standard form.
(3 + 4i)/(4 - 2i)
2/9 + 11i/9
The formula W = 3t2 models the weight of a human fetus, W, in grams after t weeks, where 0 (less than or equal to) t (less than or equal to) 39. After how many weeks does the fetus weigh 588 grams?
14 weeks
Solve the absolute value equation.
2|x-3| - 6 = 10
x = -5, 11
A retiree requires an annual income of at least $9,000 from an investment paying 2.4% annual interest. How much should the retiree invest to achieve the desired return?
at least $375,000