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Chapter 8: Problem 9

Solve each of the given equations for \(x .\) Check your answers by hand or with a calculator $$0.3 x-5.5=0.2 x+2.6$$

Short Answer

Expert verified
Question: Solve the equation \(0.3x - 5.5 = 0.2x + 2.6\) and check the solution. Answer: x = 81

Step by step solution

01

Clear the decimals

To clear the decimals, we will multiply each term in the equation by 10: \((10 \times 0.3x) - (10 \times 5.5) = (10 \times 0.2x) + (10 \times 2.6)\), which simplifies to \(3x - 55 = 2x + 26\).
02

Isolate x

We begin by subtracting 2x from both sides of the equation: \((3x - 2x) - 55 = 2x - 2x + 26\), which simplifies to \(x - 55 = 26\). Next, add 55 to both sides of the equation to isolate x: \(x - 55 + 55 = 26 + 55\), which simplifies to \(x = 81\).
03

Check the solution

Now we check our solution by plugging x = 81 back into the original equation: \(0.3(81) - 5.5 = 0.2(81) + 2.6\). Evaluate each side of the equation separately: - Left side: \(0.3(81) - 5.5 = 24.3 - 5.5 = 18.8\) - Right side: \(0.2(81) + 2.6 = 16.2 + 2.6 = 18.8\) Since both sides are equal, our solution x = 81 is correct.

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