Let's solve the inequality step by step.
The given inequality is:
[tex]\[
-7p - 4 > 26p - 94
\][/tex]
First, we need to get all the terms involving [tex]\( p \)[/tex] on one side of the inequality. We'll move the [tex]\( 26p \)[/tex] term to the left side by subtracting [tex]\( 26p \)[/tex] from both sides:
[tex]\[
-7p - 26p - 4 > -94
\][/tex]
Next, we combine the like terms involving [tex]\( p \)[/tex]:
[tex]\[
-33p - 4 > -94
\][/tex]
Now, we need to isolate the term with [tex]\( p \)[/tex]. We do this by adding 4 to both sides of the inequality:
[tex]\[
-33p - 4 + 4 > -94 + 4
\][/tex]
[tex]\[
-33p > -90
\][/tex]
To solve for [tex]\( p \)[/tex], we divide both sides of the inequality by [tex]\(-33\)[/tex]. When we divide by a negative number, the direction of the inequality reverses:
[tex]\[
p < \frac{-90}{-33}
\][/tex]
Simplifying the fraction [tex]\( \frac{-90}{-33} \)[/tex]:
[tex]\[
p < \frac{90}{33}
\][/tex]
The fraction [tex]\( \frac{90}{33} \)[/tex] can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{90 \div 3}{33 \div 3} = \frac{30}{11}
\][/tex]
So, the solution to the inequality is:
[tex]\[
p < \frac{30}{11}
\][/tex]
In decimal form, this is approximately:
[tex]\[
p < 2.727272727272727
\][/tex]
But we prefer the exact fraction form:
[tex]\[
p < \frac{30}{11}
\][/tex]
