3P+(2-3P)>28
show work with answer please because I don't understand how to do this inequality.
3p + 2 - 3p > 28
2 > 28
which is an obvious contradiction, so the above inequation has no solution, since no value of p can make 2 > 28
OK that's what I thought but the textbook says the answer is p>13 which makes no sense. Thanks
To solve the inequality 3P + (2 - 3P) > 28, we can follow these steps:
Step 1: Simplify the expression inside the parentheses.
2 - 3P becomes just 2 - 3P.
Step 2: Apply the distributive property by multiplying 3P with both terms inside the parentheses.
3P + (2 - 3P) becomes 3P + 2 - 9P.
Step 3: Combine like terms (3P and -9P) to simplify the expression.
3P - 9P + 2 becomes -6P + 2.
Step 4: Rewrite the inequality with the simplified expression.
-6P + 2 > 28.
Step 5: Isolate the variable by moving the constant term (2) to the other side of the inequality.
Subtract 2 from both sides of the inequality to get -6P > 26.
Step 6: Divide both sides of the inequality by the coefficient of P (-6) to solve for P. Remember, when dividing or multiplying an inequality by a negative number, the inequality sign must be flipped.
Dividing both sides by -6 gives us P < 26/(-6), which simplifies to P < -13/3 or P < -4.33 (rounded to two decimal places).
So, the solution to the inequality 3P + (2 - 3P) > 28 is P < -4.33.