Solve the given inequality. describe the solution set using the set builder or interval notation. then graph the solution set on a number line. 3(x-5)> 6

THIRD OPTION.

Step-by-step explanation:

Given the following inequality:

You can follow these steps in order to solve it:

1. Apply Distributive property on the left side:

2. Add 15 to both sides of the inequality:

3. Finally, divide both sides of the inequality by 3:

 The symbol is means "Greater than or equal to", and indicates that 7 is  include in the solution.

Therefore, the solution can be expressed as:

Now you must mark this point with a closed dot on the number line and shade everything to the right.

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

sine

step-by-step explanation: