# How do you write an inequality and solve given "seven tenths of a number plus 14 is less than forty nine"?

May 11, 2017

$x < 50$

#### Explanation:

$\text{let the number be } x$

$\Rightarrow \frac{7}{10} x + 14 < 49 \leftarrow \text{ is the inequality to be solved}$

$\text{to eliminate the fraction, multiply ALL terms by 10}$

$\cancel{10} \times \frac{7}{\cancel{10}} x + \left(10 \times 14\right) < \left(10 \times 49\right)$

$\Rightarrow 7 x + 140 < 490$

$\text{subtract 140 from both sides}$

$7 x \cancel{+ 140} \cancel{- 140} < 490 - 140$

$\Rightarrow 7 x < 350$

$\text{divide both sides by 7}$

$\frac{\cancel{7} x}{\cancel{7}} < \frac{350}{7}$

$\Rightarrow x < 50$

$\textcolor{b l u e}{\text{As a check}}$

$\text{Select a value for " x < 50 ," say 40}$

$\Rightarrow \frac{7}{10} \times 40 + 14 = 28 + 14 = 42 < 50 \textcolor{red}{\text{ true}}$