QuestionFind the minimum value of $9x - 11$ given that $x \geq \frac{19}{3}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $9x -11$ . The constraint on $x$ is $7 \leq \frac{}{3} + x$

STEP 2

First, we need to isolate $x$ in the inequality. We can do this by subtracting $\frac{2}{}$ from both sides.
$7 - \frac{2}{} \leq x$

STEP 3

Now, calculate the value of $7 - \frac{2}{3}$ .
$7 - \frac{2}{3} = \frac{21}{3} - \frac{2}{3} = \frac{19}{3}$

STEP 4

So, the inequality becomes $\frac{19}{3} \leq x$

STEP 5

Now, we need to find the least possible value of $9x -11$ under this constraint. Since $9x -11$ is a linear function and its graph is a straight line with a positive slope, the least possible value will occur at the smallest possible value of $x$ .

STEP 6

So, we substitute $x = \frac{19}{3}$ into the function $9x -11$ .
$9x -11 =9 \left(\frac{19}{3}\right) -11$

STEP 7

Calculate the value of $9 \left(\frac{19}{3}\right) -11$ .
$9 \left(\frac{19}{3}\right) -11 =57 -11 =46$ So, the least possible value of $9x -11$ when $7 \leq \frac{2}{3} + x$ is $46$ .

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