To solve for [tex]\( x \)[/tex] when the function [tex]\( h(x) = 2x + 7 \)[/tex] and given that [tex]\( h(x) = 14 \)[/tex], follow these steps:
1. Set up the equation:
[tex]\[
h(x) = 14 \implies 2x + 7 = 14
\][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
Subtract 7 from both sides of the equation to move the constant term to the right side:
[tex]\[
2x + 7 - 7 = 14 - 7 \implies 2x = 7
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{7}{2}
\][/tex]
4. Simplify the expression:
Express the fraction in its simplest form:
[tex]\[
x = 3.5
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( h(x) = 14 \)[/tex] is [tex]\( x = 3.5 \)[/tex].
