Chapter 1: Q55. (page 46)

Solve $|2 x + 11| > 1$ for $x$ .

Short Answer

Expert verified

$x > - 5 or x < - 6$ .

Step by step solution

– Description of step.

For all real numbers $p$ and $q$ , $q > 0$ ,

Case1) If $|p| < q$ then $- q < p < q$ .

Case2) If $|p| > q$ then $p > q or p < - q$ .

– Description of step.

Apply case 2 to $|2 x + 11| > 1$ which implies $2 x + 11 > 1$ or $2 x + 11 < - 1$ .

– Description of step.

Solve $2 x + 11 > 1$ . Subtract 11 from each side of $2 x + 11 > 1$ .

$\begin{matrix} 2 x + 11 - 11 > 1 - 11 \\ 2 x > - 10 \end{matrix}$

– Description of step.

Divide each side of the obtained inequality by 2.

$\begin{matrix} \frac{2 x}{2} > - \frac{10}{2} \\ x > - 5 \end{matrix}$

– Description of step.

Solve $2 x + 11 < - 1$ . Subtract 11 from each side of $2 x + 11 < - 1$ .

$\begin{matrix} 2 x + 11 - 11 < - 1 - 11 \\ 2 x < - 12 \end{matrix}$

– Description of step.

Divide each side of the obtained inequality by 2.

$\begin{matrix} \frac{2 x}{2} < - \frac{12}{2} \\ x < - 6 \end{matrix}$

Therefore, $x > - 5 or x < - 6$ .

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Solve $|2 x + 11| > 1$ for $x$ .

Short Answer

Step by step solution

– Description of step.

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Solve 2x+11>1 for x.

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Solve $|2 x + 11| > 1$ for $x$ .