2020 SWMC 6 Problems/Problem 1

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 $\boxed1$.

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