Question

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

Answer 1

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:

$-\frac{3}{4}(4x+12)$    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:

$\frac{3}{4}(4x+12)>(2x+8)$              Remove Negative sign from both signs and change order of inequality from < to >.

$\frac{12}{4}x+\frac{36}{4}>2x+8$                Factor Out Bracket on Left Hand Side

$\frac{12}{4}x+\frac{36}{4}>\frac{8}{4}x+\frac{32}{4}$             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. $x>-1$