To solve the inequality [tex]\(\frac{d}{7} + 4 \leq 0\)[/tex], follow these steps:
1. Isolate the term involving [tex]\(d\)[/tex]:
Start with the inequality:
[tex]\[
\frac{d}{7} + 4 \leq 0
\][/tex]
Subtract 4 from both sides to isolate the fraction:
[tex]\[
\frac{d}{7} \leq -4
\][/tex]
2. Solve for [tex]\(d\)[/tex]:
To eliminate the fraction, multiply both sides of the inequality by 7:
[tex]\[
d \leq -4 \times 7
\][/tex]
Calculate [tex]\(-4 \times 7\)[/tex]:
[tex]\[
d \leq -28
\][/tex]
3. Determine the interval:
The solution to the inequality [tex]\(d \leq -28\)[/tex] includes all values of [tex]\(d\)[/tex] that are less than or equal to [tex]\(-28\)[/tex]. Therefore, the interval notation for the solution is:
[tex]\[
(-\infty, -28]
\][/tex]
So, the solution to the inequality [tex]\(\frac{d}{7} + 4 \leq 0\)[/tex] is [tex]\((- \infty, -28]\)[/tex].
