Solve for x:
7x - 9 = 33

x = 6

Step-by-step explanation: To solve a problem like this we want to use our inverse operations and we want to get the x by itself.

So to do that, I am going to use my inverse order of operations meaning I am going to undo addition and subtraction first.

Since 9 is being subtracted from 7x, to get x by itself, I am going to add 9 to both sides of the equals sign

which is the addition property of equality.

The reason we add to both sides is to keep these equations equivalent.

So now I have 7x = 42.

Now we look at our variable and we can see that it's being multiplied by 7 so to undo that, we divide both sides by 7.

On the left the 7's cancel and on the right, 42 divided by 7 is 6.

So we have x = 6 which is the solution to this equation.

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

step-by-step explanation: