# How do you solve 5.6z+1.5<2.5z-4.7?

Apr 2, 2017

$z < - 2$

#### Explanation:

The inequality is still correct if we 'get rid' of the decimal by multiplying both sides by 10 giving:

$56 z + 15 < 25 z - 47$

Subtract $\textcolor{red}{25 z}$ from both sides

$\textcolor{g r e e n}{56 z \textcolor{red}{- 25 z} + 15 \text{ "<" } 25 z \textcolor{red}{- 25 z} - 47}$

$\text{ "color(green)(31z+15" "<" } - 47$
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Subtract $\textcolor{red}{15}$ from both sides

$\textcolor{g r e e n}{31 z + 15 \textcolor{red}{- 15} \text{ "<" } - 47 \textcolor{red}{- 15}}$

$\text{ "color(green)(31z" "<" } - 62$
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Divide both sides by $\textcolor{red}{31}$

$\text{ "color(green)(31/(color(red)(31)) z" "<" } - \frac{62}{\textcolor{red}{31}}$

But $\frac{31}{31} = 1 \mathmr{and} 1 \times z = z$

$\text{ } \textcolor{g r e e n}{z < - 2}$