Which inequality represents all values of x for which the quotient below is defined? the problem is down below.

To make sure the stuff under the square root is not negative, we force the (x+2) expression to be 0 or positive. Meaning that we write which solves to when we subtract 2 from both sides

At the same time, the expression (5-x) under the other root is set to be greater than 0. We do not let (5-x) be equal to zero. Why not? Because this would cause a division by zero error. You cannot have the denominator be zero.

So, 5-x > 0 turns into 5 > x or x < 5 when we isolate x. This is after adding x to both sides.

--------------------------

We have the two inequalities and x < 5 at the same time. So we're describing some number between -2 and 5, where we include -2 but exclude 5. Again we're making sure x=5 is not allowed to avoid division by zero errors.

-------------------------

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be