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Chapter 6: Problem 42

Solve and check each equation. \(100=-(x-1)+4(x-6)\)

Short Answer

Expert verified
The solution to the equation is \(x = 41\).

Step by step solution

01

Expand the equation

First, distribute where you see parentheses to simplify the equation: \(100 = -(x-1) + 4(x-6) \Rightarrow 100 = -x + 1 + 4x - 24\)
02

Combine like terms

Next, combine the like terms on the right hand side of the equation: -x + 4x gives you 3x and 1 - 24 gives you -23. So the equation becomes: \(100 = 3x - 23\)
03

Isolate the variable

Now, add 23 to both sides of the equation to isolate the variable term: \(100 + 23 = 3x - 23 + 23 \Rightarrow 123 = 3x\)
04

Solve for x

Now, finally divide by 3 on both sides to isolate \(x\): \(x =123/3 = 41\).
05

Check the solution

To check if the solution is correct, substitute \(x=41\) back into the original equation: \(100 = -(41-1) + 4(41-6)\). After simplifying, the equation results in \(100 = 100\) which is true. Thus, the solution is valid.

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