Translate IxI>= 3 into words using the definition of absolute value

Step-by-step explanation:

The absolute value of an integer is the distance that separates the number from the zero position "0", that is, the absolute value of an integer is the natural number that results from suppressing its sign.

In other words, the absolute value of a real number a, written |a|, is the same number a when it is positive or zero, and opposite of a, if a is negative.

In this case IxI>= 3 means that

This is translated as, since the absolute value of x represents the distance from zero, the solutions to this inequality are those numbers whose distances from zero are greater than or equal to 3, that is, that x is greater than or equal to 3 or x is less than or equal to -3.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

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step-by-step explanation:

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