How do you solve 2x + 3 - 4x >9?

Mar 29, 2016

$x < - 3$

Explanation:

We need to end up with just 1 of the $x ' s$ and for that to be on its own on one side of the inequality sign and everything else on the other side. It is the same process as for manipulating an equation.

collecting like terms

$\left(2 x - 4 x\right) + 3 > 9$

$- 2 x + 3 > 9$

Subtract 3 from both sides giving

$- 2 x + 0 > 9 - 3$

$- 2 x > 6$

This can only be true if $x < - 3$ as $\left(- 2\right) \times \left(- 3\right) = + 6$

Multiply through out by (-1) giving

$2 x < - 6 \text{ }$

$\textcolor{red}{\text{Notice that by multiplying by negative 1 the > becomes <}}$

$x < - \frac{6}{2}$

$x < - 3$