Algebra Examples

Solve for x x-3>3(x-1)
x-3>3(x-1)
Step 1
Simplify 3(x-1).
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Step 1.1
Rewrite.
x-3>0+0+3(x-1)
Step 1.2
Simplify by adding zeros.
x-3>3(x-1)
Step 1.3
Apply the distributive property.
x-3>3x+3-1
Step 1.4
Multiply 3 by -1.
x-3>3x-3
x-3>3x-3
Step 2
Move all terms containing x to the left side of the inequality.
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Step 2.1
Subtract 3x from both sides of the inequality.
x-3-3x>-3
Step 2.2
Subtract 3x from x.
-2x-3>-3
-2x-3>-3
Step 3
Move all terms not containing x to the right side of the inequality.
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Step 3.1
Add 3 to both sides of the inequality.
-2x>-3+3
Step 3.2
Add -3 and 3.
-2x>0
-2x>0
Step 4
Divide each term in -2x>0 by -2 and simplify.
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Step 4.1
Divide each term in -2x>0 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-2x-2<0-2
Step 4.2
Simplify the left side.
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Step 4.2.1
Cancel the common factor of -2.
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Step 4.2.1.1
Cancel the common factor.
-2x-2<0-2
Step 4.2.1.2
Divide x by 1.
x<0-2
x<0-2
x<0-2
Step 4.3
Simplify the right side.
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Step 4.3.1
Divide 0 by -2.
x<0
x<0
x<0
Step 5
The result can be shown in multiple forms.
Inequality Form:
x<0
Interval Notation:
(-,0)
x-3>3(x-1)
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