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Mathematics
Lorenzo Marquez
12 January, 03:29
2. Find the value of x
3x + 7
+3
Answers (
1
)
Sweety
12 January, 03:35
0
Answer: (x-3) / (x-7) >0
Step-by-step explanation: Find all the values where the expression switches from negative to positive by setting each factor equal to
0
and solving.
x-3=0
x-7=0
Add 3 to both sides of the equation.
x = 3
Add 7 to both sides of the equation.
x = 7
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
x = 3
x = 7
Consolidate the solutions.
x = 3, 7
Find the domain of x-3x-7.
Find the domain of x - 3x-7.
Set the denominator in
x-3x-7
equal to 0
to find where the expression is undefined.
x-7=0
Add 7 to both sides of the equation.
x=7
The domain is all values of x
that make the expression defined.
Interval Notation:
(-∞,7) ∪ (7,∞)
Use each root to create test intervals.
x< 3
3
>7
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
x< 3 True
3
x>7 True
The solution consists of all of the true intervals.
x7
The result can be shown in multiple forms.
Inequality Form:
x7
Interval Notation:
(-∞,3) ∪ (7,∞)
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