Problem 41 Use interval notation to express... [FREE SOLUTION]

Chapter 1: Problem 41

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{x}{4}-\frac{3}{2} \leq \frac{x}{2}+1$$

Short Answer

Expert verified

The solution of the given inequality is $x \geq 2$, represented in interval notation as $[2, +\infty)$.

Step by step solution

Rearrange the inequality

First, isolate the term containing the variable by subtracting $\frac{x}{2}$ from both sides. This gives $\frac{x}{4}-\frac{x}{2} \leq 1 - \frac{3}{2}$. Simplify it further to $-\frac{x}{4} \leq -\frac{1}{2}$.

Solve for x

Then, solve for x by multiplying both sides by -4 (recall that inequalities switch the direction when multiplied or divided by any negative number). This will give $x \geq 2$.

Represent solution in interval notation

The solution set in interval notation is $[2, +\infty)$. This denotes that x can be any real number, equal to or greater than 2.

Plot the solution on a number line

Lastly, plot the solution on a number line, including the point at x=2 (represented by a closed circle or a bracket), with all points to the right of this point included in the solution set since the inequality is 'greater than or equal to'.

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91影视

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{x}{4}-\frac{3}{2} \leq \frac{x}{2}+1$$

Short Answer

Step by step solution

Rearrange the inequality

Solve for x

Represent solution in interval notation

Plot the solution on a number line

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