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5. Solve ecah inequality separately:

a)  Add to both sides of inequality [tex]6b-1\le 41[/tex] number 1:

[tex]6b-1+1\le 41+1,\\ \\6b\le 42.[/tex]

Divide this inequality by 6:

[tex]b\le 7.[/tex]

b) Subtract from both sides of inequality [tex]2b+1\ge 11[/tex] number 1:

[tex]2b+1-1\ge 11-1,\\ \\2b\ge 10.[/tex]

Divide this inequality by 2:

[tex]b\ge 5.[/tex]

c) If [tex]b\le 7[/tex] and [tex]b\ge 5,[/tex] then [tex]5\le b\le 7.[/tex]

Answer 5: [tex]5\le b\le 7.[/tex]

7. Solve the double inequality [tex]3<2p-3\le 12[/tex] by adding 3 annd dividing by 2:

[tex]3+3<2p-3+3\le 12+3,\\ \\6<2p\le 15,\\ \\3<p\le 7.5.[/tex]

Answer 7: [tex]3<p\le 7.5.[/tex]


(5)

we are given two inequalities

First:

[tex]6b-1\leq 41[/tex]

we can solve for b

add both sides 1

[tex]6b-1+1\leq 41+1[/tex]

[tex]6b\leq 42[/tex]

divide both sides by 6

and we get

[tex]b\leq 7[/tex]

Second:

[tex]2b+1\geq 11[/tex]

subtract both sides 1

[tex]2b+1-1\geq 11-1[/tex]

[tex]2b\geq 10[/tex]

divide both sides by 2

[tex]b\geq 5[/tex]

now, we can combine solution

and we get

[tex]b\leq 7[/tex]

[tex]b\geq 5[/tex]

we get

[tex]5\leq b\leq 7[/tex]

or

[5,7]................Answer

(7)

[tex]3<2p-3\leq12[/tex]

Add all the sides by 3

[tex]3+3<2p-3+3\leq12+3[/tex]

[tex]6<2p\leq15[/tex]

divide all the sides by 2

[tex]3<p\leq7.5[/tex].................Answer

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