Question #0e470

Feb 2, 2018

$6 \le x$

Explanation:

After writing the inequality, solve it like a regular equation for $x$:

$3 \left(x + 3\right) \le 5 x - 3$
Distribute the $3$ on the left side:
$3 x + 9 \le 5 x - 3$

Combine like terms by subtracting $3 x$ and adding $3$ to both sides:
$12 \le 2 x$
Divide both sides by $2$:
$6 \le x$

So $6$ is the lowest possible value for $x$.
You can verify this by plugging $6$ in to see if the original statement is true: $3 \left(6 + 3\right) \le 5 \left(6\right) - 3$
$\implies 3 \left(9\right) \le 30 - 3$
$\implies 27 \le 27$
So $6$ works!

You can try it with a lower number like $5$ if you want to see if $6$ is really the lowest. (It is!)