Question

A = 4lw + bh for h

L = a(1 + ct) for c
y = x(3 - yz) for z
r = s - s1t for s1
y = 12xy + 3xz for x
x = n/m - k for k
Show that when the equation n = (a + b)c is solved for b, the result is:
a) b = n - ac/c
b) b = n/ac
c) b = (n - a)/c
d) b = (n + a)/c
Show that when L = E/R + K is solved for R, the result is:
a) R = E - LK/L
b) R = (E - L)/K
c) R = E/(L - K)
d) R = (E - K)/L

Answer 1

Solving for b in the equation n = (a + b)c results in b = (n - a)/c, and solving for R in the equation L = E/R + K results in R = E/(L - K).

Step-by-step explanation:

To solve the equation n = (a + b)c for b, we will first expand the right side and then isolate the variable b.

1. Multiply both sides by c to get rid of it on the right side: nc = ac + bc.
2. Subtract ac from both sides to get b by itself: nc - ac = bc.
3. Factor out a c from the left side: c(n - a) = bc.
4. Divide both sides by c to solve for b: (n - a)/c = b.

Therefore, the correct answer is b = (n - a)/c, which corresponds to option (c).

To solve the equation L = E/R + K for R, we follow a similar process:

1. Subtract K from both sides to move it away from the fraction: L - K = E/R.
2. Multiply both sides by R to eliminate the denominator: R(L - K) = E.
3. Divide both sides by (L - K) to isolate R: R = E/(L - K).

The answer is R = E/(L - K), which is option (c).