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Chapter 4: Problem 134

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

Short Answer

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

Step by step solution

01

Distribute coefficients on both sides

First distribute \(a\) on the left side and \(b\) on the right side. This gives: \(ax - 2a = 2bx + 3b\)
02

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: \(x(a - 2b) = 3b + 2a\)
03

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: \(x = (3b + 2a) / (a - 2b)\)

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