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the solution set of which inequality is represented by the number line below

The Solution Set Of Which Inequality Is Represented By The Number Line Below class=

Sagot :

Let's solve the last inequality

[tex]-2x+5<-3[/tex]

First, we subtract 5 from each side

[tex]\begin{gathered} -2x+5-5<-3-5 \\ -2x<-8 \end{gathered}[/tex]

Then, we divide the inequality by -2

[tex]\begin{gathered} \frac{-2x}{-2}>-\frac{8}{-2} \\ x>4 \end{gathered}[/tex]

The solution to this inequality is all the real numbers greater than 4.

[tex]\begin{gathered} 4x+6>22 \\ 4x>22-6 \\ x>\frac{16}{4} \\ x>4 \end{gathered}[/tex]

[tex]\begin{gathered} 6x-7\leq17 \\ 6x\leq17+7 \\ x\leq\frac{24}{6} \\ x\leq4 \end{gathered}[/tex]

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