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Chapter 4: Problem 13

Solve the equations and inequalities. $$\frac{x}{3}-2=\frac{2}{3}$$

Short Answer

Expert verified
x = 8

Step by step solution

01

Eliminate the fraction

Multiply every term in the equation by 3 to eliminate the fraction. This gives:\[3 \times \frac{x}{3} - 3 \times 2 = 3 \times \frac{2}{3}\]
02

Simplify

Simplify the equation by performing the multiplications:\[ x - 6 = 2\]
03

Solve for x

To isolate x, add 6 to both sides of the equation:\[ x - 6 + 6 = 2 + 6 \]This simplifies to:\[ x = 8\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fractions in equations
When you encounter fractions in equations, your first goal is often to eliminate them for easier calculations. Fractions can make equations appear more complicated and harder to manage. Here鈥檚 a simple technique to handle them: multiply every term in the equation by the denominator of the fraction.

Take this equation as an example: \(\frac{x}{3} - 2 = \frac{2}{3}\). Here, the fraction \( \frac{x}{3} \) has a denominator of 3.

Multiply every term in the equation by 3:\

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Most popular questions from this chapter

The width of a rectangle is 20 less than 3 times the length. If the perimeter is \(32 \mathrm{ft}\), find its dimensions.

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