Answer:
x>-1
Step-by-step 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:
[tex]-\frac{3}{4}(4x+12)<-(2x+8)[/tex] 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 [tex]x[/tex] as follow:
[tex]\frac{3}{4}(4x+12)>(2x+8)[/tex] Remove Negative sign from both signs and change order of inequality from < to >.
[tex]\frac{12}{4}x+\frac{36}{4}>2x+8[/tex] Factor Out Bracket on Left Hand Side
[tex]\frac{12}{4}x+\frac{36}{4}>\frac{8}{4}x+\frac{32}{4}[/tex] Make Common Denominator on Both Sides
[tex]12x+36>8x+32[/tex] Eliminate denominator to simplify and remove fractions
[tex]12x-8x>32-36[/tex] Gather equal terms on each side
[tex]4x>-4[/tex] Simplify
[tex]x>-1[/tex] Solve for [tex]x[/tex]
Thus solving the inequality gives that x is greater than -1:
i.e. [tex]x>-1[/tex]
