4. What is the system of equations that describes the following graph?

The system of inequalities is

Step-by-step explanation:

step 1

Find the equation of the dashed line with negative slope

The line passes through the points

(0,-2) and (-2,0)

Find the slope

Find the equation of the line in slope intercept form

we have

substitute

The solution of the inequality is the shaded area below the dashed line

therefore

The equation of the inequality A is

step 2

Find the equation of the dashed line with positive slope

The line passes through the points

(0,0) and (4,1)

Find the slope

Find the equation of the line (direct variation)

we have

substitute

The solution of the inequality is the shaded area above the dashed line

therefore

The equation of the inequality B is

therefore

The system of inequalities is

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.