make x the subject
y=r-qp/(x)
is the ans x=-qp/(y-r)
make the subject (p)
p+3=qp+r/(2)
is the ans p=r-6/(2-q)
To make "x" the subject in the equation y = r - qp / x, follow these steps:
Step 1: Multiply both sides of the equation by "x":
xy = xr - qp
Step 2: Move all terms with "x" to one side:
xy + qp = xr
Step 3: Factor out the "x" on the right side:
xy + qp = x * r
Step 4: Divide both sides of the equation by (r + qp):
(xy + qp) / (r + qp) = x
Step 5: Simplify the equation:
x = (xy + qp) / (r + qp)
Therefore, the answer is x = (xy + qp) / (r + qp).
Now, to make "p" the subject in the equation p + 3 = qp + r / (2), follow these steps:
Step 1: Multiply both sides of the equation by (2 - q):
(2 - q)(p + 3) = (2 - q)(qp + r / (2))
Step 2: Expand the equation:
2p - qp + 6 - 3q = qp(2 - q) + r / 2 * (2 - q)
Step 3: Combine like terms:
2p - qp + 6 - 3q = 2qp - qp^2 + r(2 - q) / 2
Step 4: Distribute the terms:
2p - qp + 6 - 3q = 2qp - qp^2 + 2r - rq / 2
Step 5: Move all terms with "p" to one side:
2p - qp = 2qp - qp^2 + 2r - rq - 6 + 3q
Step 6: Combine like terms:
2p - qp = -qp^2 + 3q + 2r - rq - 6
Step 7: Add qp^2 to both sides of the equation:
2p = qp^2 - qp + 3q + 2r - rq - 6
Step 8: Rearrange the terms:
2p = qp^2 - qp - rq + 3q + 2r - 6
Step 9: Factor out "p":
2p = p(q^2 - q - r) + 3q + 2r - 6
Step 10: Divide both sides of the equation by (q^2 - q - r):
p = (p(q^2 - q - r) + 3q + 2r - 6) / (q^2 - q - r)
Therefore, the answer is p = (p(q^2 - q - r) + 3q + 2r - 6) / (q^2 - q - r).