Question

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

Answer 1

`7x - 2`

Explanation:

`1/2(8x-6) + 1/3(9x+3)`

To simplify this, use the distributive property:

Following this image, we know that:
`color(blue)(1/2(8x-6) = (1/2 * 8x) + (1/2 * -6) = 4x - 3)`
and
`color(blue)(1/3(9x+3) = (1/3 * 9x) + (1/3 * 3) = 3x + 1)`

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

Color-code like terms:
`color(red)(4x) quadcolor(blue)(-quad3) quadcolor(red)(+quad3x) quadcolor(blue)(+quad1)`

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