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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

01

– 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.

02

– Given information.

The given inequality is:

5-m<1

03

– 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.

鈭�1鈭�5<5鈭�m鈭�5<1鈭�5鈭�6<鈭�m<鈭�4

Multiply each side by -1.

鈭�6(鈭�1)>鈭�m(鈭�1)>鈭�4(鈭�1)6>m>4

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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