Question

How do you solve `3( 2- 3x ) > 4( 1- 4x )`?

Answer 1

`x > -2/7`

Explanation:

First, we need to expand the terms within the parenthesis on each side of the equation by multiplying the by the terms outside the parenthesis:

`(color(red)(3) * 2) - (color(red)(3) * 3x) > (color(blue)(4) * 1) - (color(blue)(4) * 4x)`

`6 - 9x > 4 - 16x`

Next, we can isolate the `x` terms on the left side of the inequality and the constants on the right side of the inequality by adding the correct values to zero out the necessary terms:

`6 - 9x + color(red)(16x) - color(blue)(6) > 4 - 16x + color(red)(16x) - color(blue)(6)`

`6 - color(blue)(6) - 9x + color(red)(16x) > 4 - 16x + color(red)(16x) - color(blue)(6)`

`0 - 9x + 16x > 4 - 0 - 6`

`-9x + 16x > 4 - 6`

Then, we can combine like terms on each side of the inequality:

`(-9 + 16)x > -2`

`7x > -2`

Now, we can solve for `x` by dividing each side of the inequality by `color(red)(7)`:

`(7x)/color(red)(7) > -2/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) > -2/7`

`x > -2/7`