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Chapter 6: Problem 103

Solve each equation. \(4 x+13-\\{2 x-[4(x-3)-5]\\}=2(x-6)\)

Short Answer

Expert verified
The given equation has no solution because simplifying it results in a contradictory statement \(30=-12\). This means there is no value of x that could satisfy this equation.

Step by step solution

01

Simplify the innermost brackets

The first step is to simplify the innermost set of brackets. In the given equation, the innermost brackets are \(4(x-3)\). Multiply 4 with each term inside the brackets: \(4*x-4*3\) which gives \(4x-12\) . So, the equation simplifies to: \(4*x+13-\{2*x-(4x-12-5)\}=2*(x-6)\)
02

Simplify the remaining brackets

Now, simplify the expression within the braces. Add the numbers inside the brackets which results in \(4x-17\). Substitute this into the equation which now reads as: \(4*x+13-\{2*x-(4x-17)\}=2*(x-6)\). Simplifying further by operating subtraction inside the braces we get: \(4*x+13-(2*x-4x+17)=2*(x-6)\). This further simplifies to: \(4*x+13-(2x-4x+17)=2*(x-6)\). Further simplification leads to \(2x+30=2*(x-6)\)
03

Open last set of brackets and simplify

The next step is to open the last set of brackets on the right side. Multiply 2 with each term inside the brackets: \(2*x-2*6\). This results in: \(2x+30=2x-12\)
04

Isolate the variable

Now, bring the terms with x to one side and the constants (numbers) to the other. This will give a contradiction since eliminating \(2x\) from both sides yields \(30=-12\), which is not true. Hence, we arrive at a contradiction.

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