Certainly! Let's solve the problem step-by-step:
1. Given Function: The function provided is [tex]\( h(x) = 23x - 10 + 4 \)[/tex].
2. Simplify the Function: Simplify the expression inside the function to make it easier to work with.
[tex]\[
h(x) = 23x - 10 + 4
\][/tex]
Combine the constant terms:
[tex]\[
h(x) = 23x - 6
\][/tex]
3. Find the x-intercept: To find the x-intercept, we need to determine the value of [tex]\( x \)[/tex] where the function [tex]\( h(x) = 0 \)[/tex].
4. Set [tex]\( h(x) = 0 \)[/tex]:
[tex]\[
0 = 23x - 6
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
23x - 6 = 0
\][/tex]
Add 6 to both sides:
[tex]\[
23x = 6
\][/tex]
Divide both sides by 23:
[tex]\[
x = \frac{6}{23}
\][/tex]
6. x-intercept: The value of [tex]\( x \)[/tex] at which [tex]\( h(x) = 0 \)[/tex] is:
[tex]\[
x = \frac{6}{23}
\][/tex]
Thus, the x-intercept of the function [tex]\( h(x) = 23x - 6 \)[/tex] is approximately [tex]\( 0.26087 \)[/tex].
