How do you simplify ½(8x – 6) + (1/3)(9x + 3)?

Jul 14, 2018

$7 x - 2$

Explanation:

$\frac{1}{2} \left(8 x - 6\right) + \frac{1}{3} \left(9 x + 3\right)$

To simplify this, use the distributive property:

Following this image, we know that:
$\textcolor{b l u e}{\frac{1}{2} \left(8 x - 6\right) = \left(\frac{1}{2} \cdot 8 x\right) + \left(\frac{1}{2} \cdot - 6\right) = 4 x - 3}$
and
$\textcolor{b l u e}{\frac{1}{3} \left(9 x + 3\right) = \left(\frac{1}{3} \cdot 9 x\right) + \left(\frac{1}{3} \cdot 3\right) = 3 x + 1}$

Combine the two expressions:
$4 x - 3 + 3 x + 1$

Color-code like terms:
$\textcolor{red}{4 x} \quad \textcolor{b l u e}{- \quad 3} \quad \textcolor{red}{+ \quad 3 x} \quad \textcolor{b l u e}{+ \quad 1}$

Therefore, the expression is:
$7 x - 2$