Problem 56 Solve each inequality and graph ... [FREE SOLUTION]

Chapter 6: Problem 56

Solve each inequality and graph the solution set on a number line. \(\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{x}{10}\)

Short Answer

Expert verified

The solution to the inequality \(\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{x}{10}\) is \(x \geq -2\). The corresponding graph on a number line includes -2 and all values to the right of -2.

Step by step solution

Combine like terms

Combine like terms on both sides of the inequality. This can be done by adding \(\frac{x}{10}\) to both sides to collect all \(x\) terms on one side. The inequality becomes \(\frac{4 x}{10}+1 \geq \frac{1}{5}\)

Subtract 1 from both sides

Next, subtract 1 from both sides to isolate the term with \(x\) on one side of the equation. After subtraction, the equation becomes \(\frac{4 x}{10} \geq \frac{1}{5} - 1\)

Convert Right Side to Common Fraction

To simplify further calculation, convert \(\frac{1}{5}-1\) to a common fraction. That will give \(\frac{4 x}{10} \geq -\frac{4}{5}\)

Isolate \(x\)

Isolate \(x\) on the left side by multiplying both sides by the reciprocal of \(\frac{4}{10}\). The equation becomes \(x \geq -2\)

Graph the solution on a number line

Graph the solution \(x \geq -2\) on a number line. For this, mark -2 on the number line and fill in to the right (including -2), as \(x\) is greater than or equal to -2

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91影视

Solve each inequality and graph the solution set on a number line. \(\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{x}{10}\)

Short Answer

Step by step solution

Combine like terms

Subtract 1 from both sides

Convert Right Side to Common Fraction

Isolate \(x\)

Graph the solution on a number line

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