Solve for [tex]\( p \)[/tex].

Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

[tex]\[ -7p - 4 \ \textgreater \ 26p - 94 \][/tex]

[tex]\[ \square \][/tex]



Answer :

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]