Question

given that $f(x)=\frac{4}{5}x + 9$, find the values of $x$ that produce the given values of $f(x)$.
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$f(x)=\frac{4}{5}x + 9$
if $f(x)=21$, then $x = $
if $f(x)=1$, then $x = $
if $f(x)=13$, then $x = $

Explanation:

Step1: Set f(x)=21, isolate x term

$21 = \frac{4}{5}x + 9$
$21 - 9 = \frac{4}{5}x$
$12 = \frac{4}{5}x$

Step2: Solve for x (f(x)=21)

$x = 12 \times \frac{5}{4} = 15$

Step3: Set f(x)=1, isolate x term

$1 = \frac{4}{5}x + 9$
$1 - 9 = \frac{4}{5}x$
$-8 = \frac{4}{5}x$

Step4: Solve for x (f(x)=1)

$x = -8 \times \frac{5}{4} = -10$

Step5: Set f(x)=13, isolate x term

$13 = \frac{4}{5}x + 9$
$13 - 9 = \frac{4}{5}x$
$4 = \frac{4}{5}x$

Step6: Solve for x (f(x)=13)

$x = 4 \times \frac{5}{4} = 5$

Answer:

If $f(x)=21$, then $x=15$
If $f(x)=1$, then $x=-10$
If $f(x)=13$, then $x=5$