Math

QuestionFind all real values of xx where f(x)=0f(x)=0 for f(x)=4x37f(x)=\frac{4x-3}{7}. Enter answers as a list.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=4x37f(x)=\frac{4x-3}{7} . We are looking for the real values of xx for which f(x)=0f(x)=0

STEP 2

We set the function equal to zero and solve for xx.
f(x)=04x7=0f(x)=0 \Rightarrow \frac{4x-}{7}=0

STEP 3

To solve for xx, we first multiply both sides of the equation by7 to get rid of the denominator.
7x37=707 \cdot \frac{x-3}{7}=7 \cdot0

STEP 4

implify the equation.
4x3=04x-3=0

STEP 5

Next, we add3 to both sides of the equation to isolate the term with xx.
4x3+3=0+34x-3+3=0+3

STEP 6

implify the equation.
4x=34x=3

STEP 7

Finally, we divide both sides of the equation by4 to solve for xx.
x=34x=\frac{3}{4}So, the real value of xx for which f(x)=0f(x)=0 is x=34x=\frac{3}{4}.

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