Chapter 2: Q64. (page 62)

Solve each inequality.
$|5 - m| < 1$

Short Answer

Expert verified

The required solution of the given inequality is $4 < m < 6$ or $(4, 6)$ .

Step by step solution

– Properties of inequality.

In an absolute inequality, if $|x| < a$ , then $- a < x < a$ .

According to the subtraction property of inequality, if $a < b$ , then $a - c < b - c$ , where a,b,c are real values.

According to the multiplication property of inequality, if the inequality a<b multiplied by -1, then -a>-b, where a,b,c are real values.

– Given information.

The given inequality is:

$|5 - m| < 1$

– Use the properties of inequality to solve the given inequality.

$|5 - m| < 1$

It is an absolute inequality and it can be written as:

$- 1 < 5 - m < 1$

Subtract 5 from each side of the above inequality.

$\begin{matrix} - 1 - 5 < 5 - m - 5 < 1 - 5 \\ - 6 < - m < - 4 \end{matrix}$

Multiply each side by -1.

$\begin{matrix} - 6 (- 1) > - m (- 1) > - 4 (- 1) \\ 6 > m > 4 \end{matrix}$

This inequality can be written as:

$4 < m < 6$

The value of m lies between 4 and 6, where 4 and 6 are excluded.

Thus, the required solution of the given inequality is $4 < m < 6$ or $(4, 6)$ .

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Solve each inequality.
$|5 - m| < 1$

Short Answer

Step by step solution

– Properties of inequality.

– Given information.

– Use the properties of inequality to solve the given inequality.

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Solve each inequality.5-m<1

Short Answer

Step by step solution

– Properties of inequality.

– Given information.

– Use the properties of inequality to solve the given inequality.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each inequality.
$|5 - m| < 1$