Math, asked by sachkiratkaur2008, 2 months ago

FIND THE SOLUTION SET FOR 7< 11 - 4x < 2x + 18 , where x belong to Z.
please provide explanation.

Answers

Answered by pallavipriyadarshi20
7

Answer:

see the image for the image

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Answered by hukam0685
0

Solution set for combine inequation is C:{-1,0}.

Given:

  • 7 &lt; 11 - 4x &lt; 2x + 18 \: ,where \: x \in \: Z \\

To find:

  • Find the solution set for the inequation.

Solution:

Step 1:

Take 7<11-4x, let the solution set is A.

7 &lt; 11 - 4x \\

Subtract -11 from both sides.

7 - 11 = 11 - 4x - 11 \\

or

 - 4 &lt;  - 4x \\

Change the sign of inequation;

4 &gt; 4x \\

Divide both sides by 4.

\bf \red{ 1 &gt; x} \\

Thus,

Solution set ; A={...-2,-1,0}

Step 2:

Take last two expression, let the solution set is B.

11 - 4x &lt; 2x + 18 \\

Subtract 2x from both sides.

11 - 4x - 2x  &lt; 2x + 18 - 2x \\

or

11 - 6x = 18 \\

Subtract 11 from both sides.

 - 6x &lt; 18 - 11 \\

or

 - 6x  &lt;  7 \\

Multiply by (-1).

6x &gt;  - 7 \\

or

\bf \red{x &gt;  \frac{ - 7}{6}}  \\

Solution set,B={-1,0,1,2...}

Combine solution set is \bf C=A \cap B

Thus,

Solution set for combine inequation is C:{-1,0}.

Learn more:

1) solve the following inequality and write the solution set using interval notation

1. -9<2x+7<_19

https://brainly.in/question/11906219

2) Graph the solution set to this inequality. 3x - 11 > 7x + 9

https://brainly.in/question/41637876

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