Option A. All the real values of x where x < -1
Procedure
Solve the inequality:
(x -3)(x+1)>0
That happens in two cases.
1) When both factors >0
x-3>0 and x+1>0
x>3 and x >-1
The intersection is x >3
2) When both factors <0
x-3<0 and x+1<0
x<3 and x<-1
the intersection is x<-1.
We have obtained that the function is positive for the intervals x < -1 and x > 3. But in one of those intervals the function is decresing and in the other is increasing.
You can recognize that the function given is a parabola and, because the coefficient of the quadratic term is positive, the parabola opens upward. Then the function is decreasing in the first interval and increasing in the second interval.
Answer:
x = 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
2(x + -5) + x = x + (-6)
<u>Step 2: Solve for </u><em><u>x</u></em>
- [Distributive Property] Distribute 2: 2x - 10 + x = x - 6
- [Addition] Combine like terms (x): 3x - 10 = x - 6
- [Subtraction Property of Equality] Subtract <em>x</em> on both sides: 2x - 10 = -6
- [Addition Property of Equality] Add 10 on both sides: 2x = 4
- [Division Property of Equality] Divide 2 on both sides: x = 2
