Given that p-2q over p+2=3q ,express q in terms of p.
The answer is
C. p over 3p+8
I cant get the steps..help me
(p-2q)/(p+2) = 3q
p-2q = 3q(p+2)
p = 2q+(3p+6)q
p = (3p+8)q
q = p/(3p+8)
To find q in terms of p, we need to isolate it on one side of the equation. Here are the steps:
1. Rewrite the equation with the numerator on one side and the denominator on the other side:
(p - 2q)/(p + 2) = 3q
2. Cross-multiply to eliminate the denominator:
(p - 2q) × 1 = 3q × (p + 2)
This simplifies to:
p - 2q = 3q(p + 2)
3. Distribute 3q to both terms inside the parentheses:
p - 2q = 3pq + 6q
4. Rearrange the equation by moving 3pq and 6q terms to the left side:
p - 3pq - 6q = 2q
5. Group the terms with q on one side:
-3pq - 6q - 2q = -p
Simplify the left side:
-3pq - 8q = -p
6. Factor out q from both terms on the left side:
q(-3p - 8) = -p
7. Finally, solve for q by dividing both sides by (-3p - 8):
q = -p / (-3p - 8)
Reorder the denominator:
q = p / (3p + 8)
Therefore, the expression for q in terms of p is q = p / (3p + 8), which matches answer choice C.
To express q in terms of p, we need to isolate q on one side of the equation.
Let's start step by step:
1. Start with the given equation:
(p - 2q) / (p + 2) = 3q
2. Multiply both sides of the equation by (p + 2) to eliminate the denominator:
(p - 2q) = 3q * (p + 2)
3. Distribute 3q to both terms on the right side:
p - 2q = 3pq + 6q
4. Rearrange the equation to have all terms with q on one side:
p = 3pq + 6q + 2q
5. Combine like terms on the right side:
p = 3pq + 8q
6. Factor out q from the right side:
p = q(3p + 8)
7. Divide both sides by (3p + 8) to isolate q:
p / (3p + 8) = q
Therefore, q is equal to p divided by (3p + 8), which matches option C.