Question

puzzle #4
1: solve for d:
\frac{ab}{d} + c = e
2: solve for d:
ab - cd = e
3: solve for d:
ad + b = ce
4: solve for d:
cd - ab = e
answer choices
a: \frac{b - ce}{a}
b: \frac{ce - b}{a}
c: e + abc
d: ec - ab
e: \frac{e + ab}{c}
f: \frac{ab - e}{c}
g: \frac{abe}{c}
h: \frac{ab}{e - c}
i: \frac{ab}{c + e}
type the 4-letter code into the answer box. all caps, no spaces.

Explanation:

Sub - Question 1: Solve \(\boldsymbol{\frac{ab}{d}+c = e}\) for \(d\)

Step 1: Isolate the fraction term

Subtract \(c\) from both sides of the equation \(\frac{ab}{d}+c = e\) to get \(\frac{ab}{d}=e - c\).

Step 2: Solve for \(d\)

Take the reciprocal of both sides (or cross - multiply) to solve for \(d\). Cross - multiplying gives \(ab=(e - c)d\), then \(d=\frac{ab}{e - c}\) (which matches option H).

Sub - Question 2: Solve \(\boldsymbol{ab - cd=e}\) for \(d\)

Step 1: Isolate the term with \(d\)

Subtract \(ab\) from both sides: \(-cd=e - ab\).

Step 2: Solve for \(d\)

Multiply both sides by \(- 1\) to get \(cd = ab - e\), then divide both sides by \(c\) (assuming \(c
eq0\)): \(d=\frac{ab - e}{c}\) (which matches option F).

Sub - Question 3: Solve \(\boldsymbol{ad + b=ce}\) for \(d\)

Step 1: Isolate the term with \(d\)

Subtract \(b\) from both sides: \(ad=ce - b\).

Step 2: Solve for \(d\)

Divide both sides by \(a\) (assuming \(a
eq0\)): \(d=\frac{ce - b}{a}\) (which matches option B).

Sub - Question 4: Solve \(\boldsymbol{cd - ab = e}\) for \(d\)

Answer:

1. H
2. F
3. B
4. E

The 4 - letter code is H F B E (arranged in order of sub - questions 1 - 4), so the final answer is H F B E (in all caps, no spaces) \boxed{HFBE}