Question

solve the equation, if possible. check the result. (if there is no solution, enter no
\frac{3(b + 5)}{2} = \frac{3b - 12}{4}
learn it: solve linear equations in one variable that require simplif
enter an exact number.

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{3(b + 5)}{2}=\frac{3b-12}{4}\), we cross - multiply. Cross - multiplying gives us \(4\times3(b + 5)=2\times(3b - 12)\).

Step2: Simplify both sides

First, simplify the left - hand side: \(12(b + 5)=12b+60\) (using the distributive property \(a(b + c)=ab+ac\) where \(a = 12\), \(b=b\), and \(c = 5\)).
Then, simplify the right - hand side: \(2\times(3b-12)=6b-24\) (using the distributive property \(a(b - c)=ab - ac\) where \(a = 2\), \(b = 3b\), and \(c=12\)).
So our equation becomes \(12b + 60=6b-24\).

Step3: Subtract \(6b\) from both sides

Subtract \(6b\) from both sides of the equation \(12b + 60=6b-24\). We get \(12b-6b + 60=6b-6b-24\), which simplifies to \(6b+60=-24\).

Step4: Subtract 60 from both sides

Subtract 60 from both sides of the equation \(6b + 60=-24\). We have \(6b+60 - 60=-24-60\), which simplifies to \(6b=-84\).

Step5: Divide both sides by 6

Divide both sides of the equation \(6b=-84\) by 6. \(\frac{6b}{6}=\frac{-84}{6}\), so \(b=-14\).

Answer:

\(b = - 14\)