For what values of p is the value of the binomial 1.5p−1 smaller than the value of the binomial 1+1.1p by 4?
To find the values of p that satisfy the given condition, we can set up the following inequality:
1.5p - 1 < 1 + 1.1p - 4
First, let's simplify this inequality:
1.5p - 1 < 1 + 1.1p - 4
Combine like terms:
1.5p - 1 < 1.1p - 3
Next, let's isolate the p term by subtracting 1.1p from both sides:
1.5p - 1 - 1.1p < 1.1p - 3 - 1.1p
Simplify:
0.4p - 1 < -3
Now, let's isolate the p term by adding 1 to both sides:
0.4p - 1 + 1 < -3 + 1
Simplify:
0.4p < -2
Finally, let's divide both sides by 0.4 to solve for p:
0.4p / 0.4 < -2 / 0.4
Simplify:
p < -5
Therefore, the values of p that satisfy the given condition are any values less than -5.
To find the values of p for which the value of the binomial 1.5p - 1 is smaller than the value of the binomial 1 + 1.1p by 4, we can set up an equation and solve for p. Here's how:
1. Write the equation: 1.5p - 1 < (1 + 1.1p) - 4
2. Simplify the equation by adding 4 to both sides: 1.5p + 3 < 1 + 1.1p
3. Combine like terms: 1.5p - 1.1p < 1 - 3
4. Simplify further: 0.4p < -2
5. Divide both sides by 0.4 to isolate p: p < -2 / 0.4
6. Calculate the division: p < -5
Therefore, the values of p for which the value of the binomial 1.5p - 1 is smaller than the value of the binomial 1 + 1.1p by 4 are any values of p that are less than -5.
1+1.1p - (1.5p - 1) = 4
1 + 1.1p - 1.5p + 1 = 4
-.4p = 2
p = - 5
check:
1.5(-5) - 1 = -8.8
1+1.1(-5) = -4.5
their difference is 4