Let's solve the problem step-by-step:
1. You are given the function [tex]\( f(x) = \frac{5}{2} x + 7 \)[/tex].
2. You are also given that [tex]\( f(x) = -13 \)[/tex]. Therefore, we need to find [tex]\( x \)[/tex] such that [tex]\( f(x) = -13 \)[/tex].
3. Substitute [tex]\(-13\)[/tex] for [tex]\( f(x) \)[/tex] in the equation:
[tex]\[
\frac{5}{2} x + 7 = -13
\][/tex]
4. To isolate the term involving [tex]\( x \)[/tex], first subtract 7 from both sides of the equation:
[tex]\[
\frac{5}{2} x + 7 - 7 = -13 - 7
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{5}{2} x = -20
\][/tex]
5. Now, to solve for [tex]\( x \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\( \frac{5}{2} \)[/tex], which is [tex]\( \frac{2}{5} \)[/tex]:
[tex]\[
x = -20 \times \frac{2}{5}
\][/tex]
6. Simplify the right-hand side:
[tex]\[
x = -8
\][/tex]
So, the value of [tex]\( x \)[/tex] that satisfies [tex]\( f(x) = -13 \)[/tex] is [tex]\( x = -8 \)[/tex].
