Problem 134 - College Algebra Essentials

Question

Will help you prepare for the material covered in the next section. Solve for \(x: a(x-2)=b(2 x+3)\)

Step-by-Step Solution

Answer

The solution for the equation is \(x = (3b + 2a) / (a - 2b)\), under the condition that \(a - 2b\) must not equal zero.

Step 1: Distribute coefficients on both sides

First distribute \(a\) on the left side and \(b\) on the right side. This gives: \(ax - 2a = 2bx + 3b\)

Step 2: Rearrange terms containing \(x\)

Isolate \(x\) terms on one side of the equation and the constants on the other side. It gives: \(ax - 2bx = 3b + 2a\) or simplified: \(x(a - 2b) = 3b + 2a\)

Step 3: Solve for \(x\)

Finally, solve for \(x\) by dividing both sides of the equation by \(a - 2b\) , bearing in mind that \(a - 2b\) must not equal zero. It gives us: \(x = (3b + 2a) / (a - 2b)\)