How do you solve and graph the solution set of $| 2 x - 1 | \leq 2$ $|2x-1|<=2$ ?

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How do you solve and graph the solution set of $| 2 x - 1 | \leq 2$ $|2x-1|<=2$ ?

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Answer 1 · 2016-11-08T01:00:06

The solution of the inequality is $- 0.5 \leq x \leq 1.5$ $-0.5 <= x <= 1.5$ .

Explanation:

When solving an absolute value inequality, the process used actually depends upon which inequality symbol is in the original inequality. If the inequality symbol is $<$ $<$ or $\leq$ $<=$ , solve using an "and" compound inequality. If the inequality symbol is $>$ $>$ or $\geq$ $>=$ , solve using an "or" compound inequality. Since this inequality has a $\leq$ $<=$ symbol, it will be solved using an "and" compound inequality.

$| 2 x - 1 | \leq 2$ $|2x - 1| <= 2$

$- 2 \leq 2 x - 1 \leq 2$ $-2 <= 2x - 1 <= 2$

$- 2 + 1 \leq 2 x - 1 + 1 \leq 2 + 1$ $-2 + 1 <= 2x - 1 + 1 <= 2 + 1$

$- 1 \leq 2 x \leq 3$ $-1 <= 2x <= 3$

$\frac{- 1}{2} \leq \frac{2 x}{2} \leq \frac{3}{2}$ $(-1)/2 <= (2x)/2 <= 3/2$

$- 0.5 \leq x \leq 1.5$ $-0.5 <= x <= 1.5$

To graph this solution, put closed dots at $- 0.5$ $-0.5$ and $1.5$ $1.5$ and shade the number line between the dots.

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How do you solve and graph the solution set of $| 2 x - 1 | \leq 2$ $|2x-1|<=2$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you solve and graph the solution set of |2x−1|≤2|2x-1|<=2?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve and graph the solution set of $| 2 x - 1 | \leq 2$ $|2x-1|<=2$ ?