Solve for p: 7/12p + 14 = -5/6p - 20
To solve for p, we can start by combining like terms on both sides of the equation.
First, let's get rid of the fractions by multiplying every term by the least common denominator, which is 12.
12 * (7/12p) + 12 * 14 = 12 * (-5/6p) + 12 * (-20)
Simplifying:
7p + 168 = -10p - 240
Next, let's bring all the p terms to one side of the equation by adding 10p to both sides:
7p + 10p + 168 = -10p + 10p - 240
Simplifying:
17p + 168 = -240
Now, let's isolate p by subtracting 168 from both sides:
17p + 168 - 168 = -240 - 168
Simplifying:
17p = -408
Finally, let's solve for p by dividing both sides by 17:
p = -408 / 17
p ≈ -24.00
To solve for p in the equation 7/12p + 14 = -5/6p - 20, we can follow these steps:
Step 1: Combine like terms
First, we need to combine the terms that have p.
7/12p + 5/6p + 14 = -20
To combine these terms, we need to have a common denominator. The least common denominator (LCD) of 12 and 6 is 12. So, we rewrite the fractions with a denominator of 12:
(7/12)(12/12)p + (5/6)(2/2)p + 14 = -20
This simplifies to:
7p/12 + 10p/12 + 14 = -20
Now, we can combine the fractions:
(7p + 10p) / 12 + 14 = -20
17p / 12 + 14 = -20
Step 2: Isolate the variable
Next, we need to isolate the variable p. To do this, we can subtract 14 from both sides of the equation:
17p / 12 = -20 - 14
17p / 12 = -34
Step 3: Solve for p
To solve for p, we can multiply both sides of the equation by the reciprocal of 17/12, which is 12/17:
(12/17)(17p / 12) = (12/17)(-34)
p = -408/17
Therefore, the solution for p is -408/17.