Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2020 SWMC 6 Problems/Problem 1"
 
Line 10: Line 10:
 
<cmath>9x+5\leq14.</cmath>
 
<cmath>9x+5\leq14.</cmath>
  
−
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>.
+
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 06:52, 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 $x\leq1$. Therefore the only positive value of $x$ is $\boxed1$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2020_SWMC_6_Problems/Problem_1&oldid=135440"