Difference between revisions of "2020 SWMC 6 Problems/Problem 1"

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STOP TRYING TO CHEAT. AoPS CAN TRACK YOUR DEVICES IF YOU EDIT THIS PAGE. --aops-g5-gethsemanea2, Organizer and Creator of the SWMC contests
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==Problem==
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Give the only positive value of <math>x</math> in <math>10x + 5 \leq 14 + x</math>.
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==Solution==
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To figure out all possible values of <math>x</math>, we have to solve the inequality.
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First, we have to make sure that only one side has the variable x. To do that, we subtract x from both sides so only the left side has x in it. We have
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<cmath>9x+5\leq14.</cmath>
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Subtracting 5 from both sides gets <math>9x\leq9</math>, so x1. Therefore the only positive value of <math>x</math> is <math>\boxed1</math>.

Revision as of 05:51, 20 October 2020

Problem

Give the only positive value of $x$ in $10x + 5 \leq 14 + x$.

Solution

To figure out all possible values of $x$, we have to solve the inequality.

First, we have to make sure that only one side has the variable x. To do that, we subtract x from both sides so only the left side has x in it. We have

\[9x+5\leq14.\]

Subtracting 5 from both sides gets $9x\leq9$, so x1. Therefore the only positive value of $x$ is $\boxed1$.

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