Solve for x: 5x + one third (3x+6) > 14

Question: 5x + 1/3(3x+6) >14

First step, distribute:
5x + 1x +2>14

And combine x’s:
6x+2>14

Next, bring 2 to the other side (sign will change to negative):
6x>14-2
6x>12

Last step, bring 6 to the other side dividing 12 by 6:
x>12/6
x>3

Therefore, your answer is x>3.

Let me know if you have any further questions.

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Answer

1 number

explanation

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.