How do i solve this?

x = 2

Step-by-step explanation:

Set up a proportion. Use the big triangle (whose left side is 6 + 4) and the top triangle.

6/(6 + 4) = (x + 1) / (x + x+1)

6/10 = (x + 1 ) / (2x + 1)                Reduce the left side

3/5 = (x + 1) / (2x + 1)                  Cross Multiply

3*(2x + 1) = 5*(x + 1)                    Remove the brackets

6x + 3 = 5x + 5                           Subtract 5x from both sides

6x-5x + 3 = 5                              Combine the left

x + 3 = 5                                      Subtract 3 from both sides

x = 2

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is