Question

I need tutor answer this two quedtion thabks you so much

Answer 1

5. Let the following inequality:

`13-3m\text{ }<-2`

this is equivalent to:

`-13+3m\text{ }>2`

this is equivalent to:

`-13+13+3m\text{ }>2\text{ +13}`

this is equivalent to:

`3m\text{ }>15`

solve for m:

`m\text{ }>(15)/(3)=5`

that is :

`m\text{ }>5`

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

`(-\infty,-3\rbrack\text{ = x}\leq-3`

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

a) Let the inequality

`(x)/(3)+2\leq1`

this is equivalent to:

`(x)/(3)+2-2\leq1-2`

this is equivalent to:

`(x)/(3)\leq-1`

solve for x:

`x\leq-3`

then. A) represent the graph.

b)Let the inequality

`8-5x\ge23`

this is equivalent to:

`-8+5x\leq-23`

this is equivalent to:

`-8+8+5x\leq-23+8`

this is equivalent to:

`5x\leq-15`

solve for x:

`x\leq(-15)/(5)\text{ = -3}`

then the solution interval would be:

`x\leq\text{-3}`

then. B) represent the graph.

c) Let the inequality:

`-18\ge3+7x`

this is equivalent to:

`-18+18\ge3+18+7x`

this is equivalent to:

`0\ge21+7x`

this is equivalent to:

`-21\ge7x`

solve for x:

`x\text{ }\leq(-21)/(7)\text{ = -3}`

that is:

`x\text{ }\leq\text{-3}`

then. C) represent the graph.

d) Let the inequality:

`7x-3\leq18`

this is equivalent to:

`7x-3+3\leq18+3`

this is equivalent to:

`7x\leq21`

solve for x:

`x\leq3`

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

`x\leq3\text{ }\\e\text{ }x\leq-3\text{ }`

Finally:

e) Let the inequality:

`1-(x)/(2)\text{ }\leq2\text{ +}(1)/(2)`

this is equivalent to:

`-1+(x)/(2)\text{ }\ge-2\text{ -}(1)/(2)`

this is equivalent to

`-2+x\text{ }\ge-4\text{ -}1`

that is:

`x\text{ }\ge-4\text{ -}1+2`

that is:

`x\text{ }\ge-3`

THEN WE CAN CONCLUDE THAT THE CORRECT ANSWER ARE:

A), B), C) AND E)