Algebra--Correction?

Solve x^2 -3x is greater than or equal to 10

Would the solutions be x=5 and x= -2?

Here's how I figured it.
x^2-3x is greater than or equal to 10.
I subtracted 10 from both sides. This left me with x^2-3x-10 is greater than or equal to 0. Next, I factored and came up with (x-5)(x+2) is greater than or equal to 0. Logically, it would follow that x=5 and x= -2 would it not? And then in symbolic form my answer would read x is less than or equal to -2 OR x is greater than or equal to 5.

Where, exactly, did I go wrong?

  1. 👍 0
  2. 👎 0
  3. 👁 508
  1. You can start with:
    "(x-5)(x+2) is greater than or equal to 0"

    The part " x=5 and x= -2" is only part of the solution, namely the equality part.
    You still have to solve the inequality part.

    There are two ways to look at this.
    First, the easy way witout any calculatoins. For a parabola with the leading coefficient (1)x² >0, we know that the curve is concave upwards, so the values of x between these two zeroes must be less than zero. The answer should therefore be:
    (-∞,-2]∪[5,∞), or
    x≤-2 or x≥5.

    The second way is to assign values of x close to but not equal to the zeroes.
    f(-10) = 120
    f(-2.1) = 0.71
    f(-1.9) = -0.69
    f(0) = -10
    f(4.9) = -0.69
    f(5.1) = 0.71
    f(10) = 60
    It is clear then that for f(x) = x²-3x-10 ≥ 0,
    x ≤ -2 or x ≥ 5

    1. 👍 0
    2. 👎 0
  2. Please don't start a new post for a question if you have a second part to the same problem.
    Also give yourself a "First Name", it is much easier to keep track of replies.

    Now to your question,
    you had
    (x-5)(x+2) < 0
    I showed you a simple way to proceed from there, but apparently you did not understand it.

    so here is the "formal" way
    We are multiplying two factors and the result is negative ( < 0)
    so one must be positive , the other negative but we don't know which one, so

    1. x-5 > 0 AND x+2< 0
    x>0 AND x < -2

    OR

    2. x-5<0 AND x+2>0
    x<5 AND x>-2

    clearly the first case is not possible,
    Can you think of a number which is greater than 2 AND less than -2 ? There is none

    Since the two cases are separated by OR, the second case is true.
    now recall that the symbold was ≤ and ≥ so we have to include the -2 and 5
    and my solution would be all values between -2 and 5 inclusive or
    -2 ≤ x ≤ 5, as I stated earlier.

    1. 👍 0
    2. 👎 0
  3. ARGLHHHH!!!

    After all that I messed up by reading your question as
    ≤ instead of ≥

    Please follow MathMate's solution, he is right.

    1. 👍 0
    2. 👎 0
  4. Haha... I was about to say, I'm a bit confused...

    In other words, I'm correct?
    I said x is less than or equal to -2 OR x is greater than or equal to 5.
    MathMate concluded with x ≤ -2 or x ≥ 5 ; both mean the same.. or so I thought.

    1. 👍 0
    2. 👎 0
  5. Yes, your last sentence is correct.
    I have mis-read your answer as:
    "it would follow that x=5 and x= -2 would it not" meaning only equality.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    An isosceles triangle has at least two congruent sides.the perimeter of a certain isosceles triangle is at most 12in. The length of each of the two congruent sides is 5in . What are possible lengths of the remaining side? A.s

  2. Math

    please check my work. 1. The number of words (x) Tina can type per minute is at Least 50. write and graph and inequality. (I broke it down to these 2 choices because the A & D was incorrect) B. x is less than or equal to 50 C. x

  3. math

    7. The tennis team is selling key chains as a fundraiser. If its goal is to raise is at least 180, how many key chains must it sell at $2.25 each to meet that goal? Write and solve an inequality. a. 2.25k (greater than or equal

  4. Math

    Hi everyone, my name is Emerson. I was wondering if anybody could help me on a test. I'm stuck on some, but I think I know some others. Thank you! 1. Translate the phrase "nine more than two times a number" in to an algebraic

  1. Intermediate Algebra

    Find the maximum value of the objective function and the values of x and y for which it occurs. F = 5x + 2y x + 2y (greater than or equal to) 6 2x + y (greater than or equal to) 6 Both x and y are greater than or equal to 0. I

  2. Algebra 2 A

    What is the minimum value for z=3x-1/2y over the feasibility region defined by the constraints? a.-4 b.-5 c.-3 d.-6 constraints x greater than or equal to 0 y less than or equal to 8 y greater than or equal to x y greater than or

  3. Calculus

    Show that the curve y=6x^3+5x-3 has no tangent line with slope 4. The answer key says that m=y'=18x^2+5, but x^2 is greater than or equal to 0 for all x, so m is greater than or equal to 5 for all x. I don't understand that x^2 is

  4. Math help

    Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.

  1. Math help please!

    Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions. Okay so that is the question, I know it's already on

  2. Algebra 1 (Reiny)

    1). Describe the solutions of 1/3x => 2 in words. A: The solutions of 1/3x => 2 are all real numbers greater than or equal to 2? 2). Citizens less than 18 years old are not allowed to vote. Define a variable and write an

  3. math

    Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions. I have no idea?

  4. algabra

    Note: Remember to show all of the steps that you use to solve the problem. You have $59.95 in your wallet and want to buy some new CDs. If the CDs are $11.99 each, what number of CDs, x, can you buy? Write and solve an inequality.

You can view more similar questions or ask a new question.