how do i solve this one?

In this question, you're solving for x.

Solve for x:

2(x - 8) + 4x = 6(x - 2) - 4

Distribute the 2 to the variables inside the parenthesis.

2x - 16 + 4x = 6(x - 2) - 4

Distribute the 6 to the variables inside the parenthesis.

2x - 16 + 4x = 6x - 12 - 4

6x - 16 = 6x - 12 - 4

6x - 16 = 6x - 16

Subtract 6x from both sides

-16 = -16

Add 16 to both sides

0 = 0

All real numbers and solutions

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.