How do you solve -9 < 4x + 3 < 11?

Aug 29, 2015

$- 3 < x < 2$

Explanation:

Given
$\textcolor{w h i t e}{\text{XXXX}} - 9 < 4 x + 3 < 11$

Things you can do with expressions in an inequality which maintain the inequality:

• Add the same amount to each expression
• Subtract the same amount from each expression
• Divide each expression by the same amount provided the amount is greater than zero
• Multiply each expression by the same amount provided the amount is greater than zero

So, we can subtract $3$ from each expression, to get:
$\textcolor{w h i t e}{\text{XXXX}} - 12 < 4 x < 8$

Then we can divide each expression by $4$, to get:
$\textcolor{w h i t e}{\text{XXXX}} - 3 < x < 2$