Algebra Examples

Solve the Inequality for x 10^(4x+1)>=100^(x-2)
Step 1
Create equivalent expressions in the equation that all have equal bases.
Step 2
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Step 3
Solve for .
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Step 3.1
Simplify .
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Step 3.1.1
Rewrite.
Step 3.1.2
Simplify by adding zeros.
Step 3.1.3
Apply the distributive property.
Step 3.1.4
Multiply by .
Step 3.2
Move all terms containing to the left side of the inequality.
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Step 3.2.1
Subtract from both sides of the inequality.
Step 3.2.2
Subtract from .
Step 3.3
Move all terms not containing to the right side of the inequality.
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Step 3.3.1
Subtract from both sides of the inequality.
Step 3.3.2
Subtract from .
Step 3.4
Divide each term in by and simplify.
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Step 3.4.1
Divide each term in by .
Step 3.4.2
Simplify the left side.
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Step 3.4.2.1
Cancel the common factor of .
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Step 3.4.2.1.1
Cancel the common factor.
Step 3.4.2.1.2
Divide by .
Step 3.4.3
Simplify the right side.
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Step 3.4.3.1
Move the negative in front of the fraction.
Step 4
Use each root to create test intervals.
Step 5
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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Step 5.1
Test a value on the interval to see if it makes the inequality true.
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Step 5.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 5.1.2
Replace with in the original inequality.
Step 5.1.3
The left side is equal to the right side , which means that the given statement is always true.
True
True
Step 5.2
Test a value on the interval to see if it makes the inequality true.
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Step 5.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 5.2.2
Replace with in the original inequality.
Step 5.2.3
The left side is greater than the right side , which means that the given statement is always true.
True
True
Step 5.3
Compare the intervals to determine which ones satisfy the original inequality.
True
True
True
True
Step 6
The solution consists of all of the true intervals.
or
Step 7
Combine the intervals.
All real numbers
Step 8
The result can be shown in multiple forms.
All real numbers
Interval Notation:
Step 9