Question

Solving Literal Equations
Solve for the indicated variable:
3a + 60 = 4 for b.

Answer 1

To find b subtract 60 from both sides to isolate 3a, then divide by 4. The solution is
`\(b = (3a + 60)/(4)\)`.

Step-by-step explanation:

To solve the equation 3a + 60 = 4 for b, we need to isolate \(b\) on one side of the equation. Begin by subtracting 60 from both sides to isolate the term with a:

3a = 4 - 60

Simplify the right side of the equation:

3a = -56

Now, divide both sides by 3 to solve for a:

`\[ a = (-56)/(3) \]`

Now that we have the value for a, substitute it back into the original equation to solve for b:

`\[ b = (3 \left((-56)/(3)\right) + 60)/(4) \]`

Simplify the expression further:

`\[ b = (-56 + 60)/(4) \]`

Combine like terms:

`\[ b = (4)/(4) \]`

Finally, simplify to get the value of \(b\):

b = 1

Therefore, the solution to the equation 3a + 60 = 4 for b is b = 1. This means that when a is
`\((-56)/(3)\),`the equation holds true.