Kiana Dodson

2022-06-20

How do you write an inequality and solve given "two thirds of a number added to six is at least twenty two"?

America Barrera

Step 1
$\text{two-thirds of a number}\phantom{\rule{1ex}{0ex}}\to \frac{2}{3}x$
$\text{added to}\phantom{\rule{1ex}{0ex}}6\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to 6+\frac{2}{3}x$
'Is at least' 22 means it can be equal to 22, or more than 22.
$6+\frac{2}{3}x\ge 22$
$\frac{2}{3}x\ge 22-6$
$\frac{2}{3}x\ge 16$
$\frac{3}{2}×\frac{2}{3}x\ge \frac{3}{2}×16$
$x\ge 24$

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