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Math  /  Algebra

Question43−b3=5943-\frac{b}{3}=59

Studdy Solution

STEP 1

1. The equation 43−b3=59 43 - \frac{b}{3} = 59 is asking us to solve for b b .
2. This is a linear equation involving basic algebraic operations.
3. We will isolate the variable b b by performing inverse operations.

STEP 2

1. Isolate the term involving the variable b b .
2. Eliminate the fraction to solve for b b .
3. Check the solution by substituting it back into the original equation.

STEP 3

First, we need to isolate the term involving b b . To do this, subtract 43 from both sides of the equation:
43−b3−43=59−43 43 - \frac{b}{3} - 43 = 59 - 43
Simplifying this gives:
−b3=16 -\frac{b}{3} = 16

STEP 4

Now, eliminate the fraction by multiplying both sides of the equation by −3-3 to solve for b b :
−3×(−b3)=16×(−3) -3 \times \left(-\frac{b}{3}\right) = 16 \times (-3)
This simplifies to:
b=−48 b = -48

STEP 5

Check the solution by substituting b=−48 b = -48 back into the original equation:
43−−483=59 43 - \frac{-48}{3} = 59
Simplify the fraction:
43+16=59 43 + 16 = 59
Since both sides of the equation are equal, the solution is verified.
The solution is:
−48 \boxed{-48}

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