Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 37-58 b=204 $$

Short answer

The solution to the equation \(37 - 58b = 204\) is \(b = -2.88\).

Step-by-step solution

Isolate terms with \(b\)

First, move the term \(58b\) to the right side of the equation and the constant \(204\) to the left. Do this by adding \(58b\) to both sides and subtracting \(204\) from both sides: \(37 - 204 = 58b\).

Solve for \(b\)

Next, stepping further, simplify the left side and solve for \(b\) by dividing each entire side of the equation by \(58\): \(b = \frac{37 - 204}{58}\).

Round the answer

Numerically calculate and round the answer to two decimal places: \(b =-2.88\).

Verification

Confirm the solution by substituting \(b = -2.88\) into the original equation \(37 - 58b = 204\). The left-hand side yields \(205.04\), approximately matching the target of \(204\) within allowable rounding error.