Question

solve the equation for a. 14 + x = 3a + ab
show hint
solve the equation for r. i = prt
○ $r = \frac{i}{pt}$
○ $r = \frac{ip}{t}$
○ $r = ipt$
solve the equation for s. p - 5 = 3s + 8
show hint

Explanation:

First Sub - Question: Solve \(14 + x=3a + ab\) for \(a\)

Step 1: Factor out \(a\) on the right - hand side

We can factor \(a\) from the terms \(3a+ab\) using the distributive property \(ac + bc=(a + b)c\) (in reverse). So, \(3a+ab=a(3 + b)\). The equation becomes \(14 + x=a(3 + b)\).

Step 2: Solve for \(a\)

To isolate \(a\), we divide both sides of the equation \(14 + x=a(3 + b)\) by \((3 + b)\) (assuming \(3 + b
eq0\)). So, \(a=\frac{14 + x}{3 + b}\).

Second Sub - Question: Solve \(i = prt\) for \(r\)

Step 1: Isolate \(r\)

We want to get \(r\) by itself. Since \(i = prt\), and \(p\) and \(t\) are multiplied by \(r\), we can divide both sides of the equation by \(pt\) (assuming \(p
eq0\) and \(t
eq0\)).

Step 2: Perform the division

Dividing both sides of \(i = prt\) by \(pt\) gives \(\frac{i}{pt}=\frac{prt}{pt}\). Simplifying the right - hand side, the \(p\) and \(t\) terms cancel out, and we get \(r=\frac{i}{pt}\). So the correct option is \(r = \frac{i}{pt}\) (the first option).

Third Sub - Question: Solve \(p-5 = 3s+8\) for \(s\)

Step 1: Subtract 8 from both sides

We start with the equation \(p - 5=3s+8\). Subtract 8 from both sides to get \(p-5 - 8=3s+8 - 8\). Simplifying the left - hand side: \(p-13 = 3s\).

Step 2: Divide both sides by 3

Now, divide both sides of the equation \(p - 13=3s\) by 3. So, \(\frac{p - 13}{3}=\frac{3s}{3}\), which simplifies to \(s=\frac{p - 13}{3}\) or \(s=\frac{p}{3}-\frac{13}{3}\).

Answer:

s:

• For \(14 + x = 3a+ab\), \(a=\boldsymbol{\frac{14 + x}{3 + b}}\) (or \(a=\frac{x + 14}{b + 3}\))
• For \(i = prt\), the answer is \(\boldsymbol{r=\frac{i}{pt}}\) (the first option: \(r=\frac{i}{pt}\))
• For \(p - 5=3s + 8\), \(s=\boldsymbol{\frac{p - 13}{3}}\) (or \(s=\frac{p}{3}-\frac{13}{3}\))