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Veronika [31]
3 years ago
14

Which of the following is the solution set for the conjunction –6 < 4x + 2 < 6? x>−32 and x<32 x >–2 and x < 1

x>−32 or x<32 x <–2 or x > 1
Mathematics
1 answer:
alisha [4.7K]3 years ago
3 0

-6

<em><u>Solution:</u></em>

<em><u>Given conjunction is:</u></em>

-6

We have to find the solution set

<em><u>Let us solve the given conjuction</u></em>

\mathrm{If}\:a

Therefore,

-6

<h3><em><u>Let us first solve -6 < 4x + 2</u></em></h3>

-6 < 4x + 2

Switch the sides by flipping the inequality symbol

4x+2>-6

\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\4x+2-2>-6-2\\\\\mathrm{Simplify}\\\\4x>-8\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4x}{4}>\frac{-8}{4}

x>-2

<h3><u><em>Now let us solve 4x + 2 < 6</em></u></h3>

4x+2

\mathrm{Combine\:the\:intervals}

x>-2\quad \mathrm{and}\quad \:x

Merge\:Overlapping\:Intervals

-2

<h3><u>Thus the solution set for  –6 < 4x + 2 < 6 is:</u></h3>

-6

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