Algebra Examples

Solve the System of Inequalities -6x>-18 and 1<=2x+5
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Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
and
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
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Step 1.2.1.2
Divide by .
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Step 1.3
Simplify the right side.
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Step 1.3.1
Divide by .
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Step 2
Simplify the second inequality.
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Step 2.1
Rewrite so is on the left side of the inequality.
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Step 2.2
Move all terms not containing to the right side of the inequality.
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Step 2.2.1
Subtract from both sides of the inequality.
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Step 2.2.2
Subtract from .
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Step 2.3
Divide each term in by and simplify.
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Step 2.3.1
Divide each term in by .
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Step 2.3.2
Simplify the left side.
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Step 2.3.2.1
Cancel the common factor of .
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Step 2.3.2.1.1
Cancel the common factor.
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Step 2.3.2.1.2
Divide by .
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Step 2.3.3
Simplify the right side.
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Step 2.3.3.1
Divide by .
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Step 3
The intersection consists of the elements that are contained in both intervals.
Step 4
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 5