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Chapter 8: Problem 10

Solve each of the given equations for \(x .\) Check your answers by hand or with a calculator $$4-0.025 x=0.1-0.05 x$$

Short Answer

Expert verified
Answer: \(x = -156\)

Step by step solution

01

Identify the equation to solve

The given equation is \(4 - 0.025x = 0.1 - 0.05x\). We have to solve for x.
02

Simplify the equation

To simplify, we will move all variables (x) to one side and constants to another side. In doing so, add \(0.05x\) to both sides and subtract \(0.1\) from both sides: \[4 - 0.025x + 0.05x = 0.1 - 0.05x + 0.05x \Rightarrow 3.9 + 0.025x = 0\]
03

Solve for x

To isolate the x term, we will divide by the coefficient of x on both sides. Divide by \(0.025\): \[\frac{3.9 + 0.025x}{0.025} = \frac{0}{0.025} \Rightarrow x = -156\]
04

Check the solution

In this step, we will substitute the \(x\) value back into the equation to check the accuracy of our solution. Our solution is \(x = -156\): \[4 - 0.025(-156) = 4 + 3.9 = 7.9\] \[0.1 - 0.05(-156) = 0.1 + 7.8 = 7.9\] As both sides of the equation are equal, our solution is correct. The value of \(x\) that satisfies the equation is \(x = -156\).

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