i need tutor answer this two quedtion thabks you so much

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25-10-2022
Mathematics

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i need tutor answer this two quedtion thabks you so much

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BakariC112322 BakariC112322 · Answer 1 · 2022-10-25T22:02:30+02:00

5. Let the following inequality:

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

this is equivalent to:

[tex]-13+3m\text{ }>2[/tex]

this is equivalent to:

[tex]-13+13+3m\text{ }>2\text{ +13}[/tex]

this is equivalent to:

[tex]3m\text{ }>15[/tex]

solve for m:

[tex]m\text{ }>\frac{15}{3}=5[/tex]

that is :

[tex]m\text{ }>5[/tex]

6. Because of the graphic (real line), we can conclude that the correct interval would be:

[tex](-\infty,-3\rbrack\text{ = x}\leq-3[/tex]

Then we have to find the inequalities that have this solution interval.

a) Let the inequality

[tex]\frac{x}{3}+2\leq1[/tex]

this is equivalent to:

[tex]\frac{x}{3}+2-2\leq1-2[/tex]

this is equivalent to:

[tex]\frac{x}{3}\leq-1[/tex]

solve for x:

[tex]x\leq-3[/tex]

then. A) represent the graph.

b)Let the inequality

[tex]8-5x\ge23[/tex]

this is equivalent to:

[tex]-8+5x\leq-23[/tex]

this is equivalent to:

[tex]-8+8+5x\leq-23+8[/tex]

this is equivalent to:

[tex]5x\leq-15[/tex]

solve for x:

[tex]x\leq\frac{-15}{5}\text{ = -3}[/tex]

then the solution interval would be:

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

then. B) represent the graph.

c) Let the inequality:

[tex]-18\ge3+7x[/tex]

this is equivalent to:

[tex]-18+18\ge3+18+7x[/tex]

this is equivalent to:

[tex]0\ge21+7x[/tex]

this is equivalent to:

[tex]-21\ge7x[/tex]

solve for x:

[tex]x\text{ }\leq\frac{-21}{7}\text{ = -3}[/tex]

that is:

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

then. C) represent the graph.

d) Let the inequality:

[tex]7x-3\leq18[/tex]

this is equivalent to:

[tex]7x-3+3\leq18+3[/tex]

this is equivalent to:

[tex]7x\leq21[/tex]

solve for x:

[tex]x\leq3[/tex]

We can conclude that this interval does not represent the graph because:

[tex]x\leq3\text{ }\ne\text{ }x\leq-3\text{ }[/tex]

Finally:

e) Let the inequality:

[tex]1-\frac{x}{2}\text{ }\leq2\text{ +}\frac{1}{2}[/tex]

this is equivalent to:

[tex]-1+\frac{x}{2}\text{ }\ge-2\text{ -}\frac{1}{2}[/tex]

this is equivalent to

[tex]-2+x\text{ }\ge-4\text{ -}1[/tex]

that is:

[tex]x\text{ }\ge-4\text{ -}1+2[/tex]

that is:

[tex]x\text{ }\ge-3[/tex]

THEN WE CAN CONCLUDE THAT THE CORRECT ANSWER ARE:

A), B), C) AND E)