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how do I do this on a line?[tex]3 \ \textless \ 2x - 3 \leqslant 13[/tex]

Sagot :

Let the inequality:

[tex]3\text{ }<\text{ 2x - 3}\leq\text{ 13}[/tex]

1. we add + 3 :

[tex]3\text{ +3}<\text{ 2x }\leq\text{ 13}+3[/tex]

this is equivalent to :

[tex]6<\text{ 2x }\leq\text{ 1}6[/tex]

we resolve for x ( we divide by 2) :

[tex]3<\text{ x }\leq8[/tex]

that is the interval:

[tex](3,\text{ 8}\rbrack[/tex]

on the real line, the interval is:

On the other hand, the inequality:

[tex]-2\text{ }<\frac{3+x}{4}\leq\text{ 3}[/tex]

1. Multiply by 4:

[tex]-8\text{ }<3+x\leq12[/tex]

2. Add -3:

[tex]-11\text{ }that is the interval:

[tex](-11,\text{ 9}\rbrack[/tex]

on the real line, the interval is:

View image BodeG550751
View image BodeG550751
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