Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
-7p-4 > 26p -94
To solve the inequality -7p - 4 > 26p - 94, we need to isolate the variable "p" on one side of the inequality sign.
First, let's simplify both sides of the inequality by combining like terms:
-7p - 4 > 26p - 94
Next, let's subtract 26p from both sides to eliminate the variable term on the right side of the inequality:
-7p - 4 - 26p > 26p - 94 - 26p
Simplifying the equation further, we have:
-33p - 4 > -94
Now, to isolate the variable "p," let's move the constant term (-4) to the right side of the inequality by adding 4 to both sides:
-33p > -94 + 4
Simplifying further, we have:
-33p > -90
Lastly, to solve for "p," we need to divide both sides of the inequality by -33. However, since we are dividing by a negative number, we also need to reverse the inequality sign:
p < (-90) / -33
Dividing -90 by -33 gives us a positive value:
p < 90/33
Therefore, the solution to the inequality -7p - 4 > 26p - 94 is:
p < 90/33.
However, we should simplify the fraction to its lowest terms. To reduce the fraction 90/33 to its lowest terms, we can find the greatest common divisor (GCD) of the numerator (90) and the denominator (33). The GCD of 90 and 33 is 3.
Dividing both the numerator and denominator of the fraction 90/33 by 3, we get:
90 ÷ 3 / 33 ÷ 3 = 30/11
Hence, the final solution to the inequality -7p - 4 > 26p - 94, after simplifying the fraction to its lowest terms, is:
p < 30/11.
add 7p both sides
-4 > 33 P - 94
add 94 both sides
90 > 33 p
divide by 3
30 >11 p
p < 30 / 11