Solve the rational inequality x-2/x + x+2/x+3 < 3/2 represent your answer using a number line and using interval notation

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01-05-2021
Mathematics

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Solve the rational inequality x-2/x + x+2/x+3 < 3/2 represent your answer using a number line and using interval notation

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Buchinnamani208idn Buchinnamani208idn · Answer 1 · 2021-05-02T23:34:41-04:00

Buchinnamani208idn Buchinnamani208idn

02-05-2021

Answer and explanation:

To solve the inequality x-2/x + x+2/x+3 < 3/2 we have to first simplify the expressions on the left side of the inequality sign. And so we multiply x by the expressions on the left side to eliminate fractions:

=x(x-2/x)+x(x+2/x)+x(3)< 3/2

=x-2+x+2+3x < 3/2

=5x < 3/2

x < 3/2/5

x < 3/2×5/1

x < 15/2

x < 7 1/2 or 7. 5

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