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

Beginner2022-06-21Added 23 answers

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.

$6+\frac{2}{3}x\ge 22$

$\frac{2}{3}x\ge 22-6$

$\frac{2}{3}x\ge 16$

$\frac{3}{2}\times \frac{2}{3}x\ge \frac{3}{2}\times 16$

$x\ge 24$

$\text{two-thirds of a number}\phantom{\rule{1ex}{0ex}}\to \frac{2}{3}x$

$\text{added to}\phantom{\rule{1ex}{0ex}}6\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to 6+\frac{2}{3}x$

'Is at least' 22 means it can be equal to 22, or more than 22.

$6+\frac{2}{3}x\ge 22$

$\frac{2}{3}x\ge 22-6$

$\frac{2}{3}x\ge 16$

$\frac{3}{2}\times \frac{2}{3}x\ge \frac{3}{2}\times 16$

$x\ge 24$