Question

-3/4(4x+12)< - (2x+8)

Answer 1

x>-1

Explanation:

We will assume that here the question prompt us to solve the Inequality given and find the value of x for which is true and valid.

To begin with, let us re write our inequality clear as:

`-(3)/(4)(4x+12)<-(2x+8)` Eqn(1).

Now, since this is an Inequality it must be noted that for any operation of multiplication/devision with a Negative number, the order of the Inequality will change from ≤ to ≥ and vice versa.

So having said that, let us solve Eqn(1) and obtain a value for
`x` as follow:

`(3)/(4)(4x+12)>(2x+8)` Remove Negative sign from both signs and change order of inequality from < to >.

`(12)/(4)x+(36)/(4)>2x+8` Factor Out Bracket on Left Hand Side

`(12)/(4)x+(36)/(4)>(8)/(4)x+(32)/(4)` Make Common Denominator on Both Sides

`12x+36>8x+32` Eliminate denominator to simplify and remove fractions

`12x-8x>32-36` Gather equal terms on each side

`4x>-4` Simplify

`x>-1` Solve for
`x`

Thus solving the inequality gives that x is greater than -1:

i.e.
`x>-1`