# Solve the Inequality for x 1/2x+3<2/3x+5/3

Solve the Inequality for x 1/2x+3<2/3x+5/3
Combine and .
Combine and .
Move all terms containing to the left side of the inequality.
Subtract from both sides of the inequality.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Subtract from .
Move to the left of .
Move the negative in front of the fraction.
Move all terms not containing to the right side of the inequality.
Subtract from both sides of the inequality.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Divide each term in by and simplify.
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.
Simplify the left side.
Dividing two negative values results in a positive value.
Divide by .
Simplify the right side.
Dividing two negative values results in a positive value.
Divide by .
Multiply both sides by .
Simplify.
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
Simplify .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
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