Difference between revisions of "2020 SWMC 6 Problems/Problem 1"
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| − | + | ==Problem== | |
| + | Give the only positive value of <math>x</math> in <math>10x + 5 \leq 14 + x</math>. | ||
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| + | ==Solution== | ||
| + | |||
| + | To figure out all possible values of <math>x</math>, 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 | ||
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| + | <cmath>9x+5\leq14.</cmath> | ||
| + | |||
| + | Subtracting 5 from both sides gets <math>9x\leq9</math>, so <math>x\leq1</math>. Therefore the only positive value of <math>x</math> is <math>\boxed1</math>. | ||
Latest revision as of 05:52, 20 October 2020
Problem
Give the only positive value of 
in 
.
Solution
To figure out all possible values of , 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
![\[9x+5\leq14.\]](http://latex.artofproblemsolving.com/0/0/c/00c299e88064f61de189219c4cfbdb97dc964572.png)
Subtracting 5 from both sides gets 
, so 
. Therefore the only positive value of is 
.
