1 Answer

David Joos · Answer 1 · 2023-10-14T03:17:21+0000

Question:

Solve and graph the compound inequality on the real numbers and write the solutions in interval notation, and provide one specific solution.

3x/4-1>x/3-3/5 and 2x-18/5>x+2/5.

Solution:

Consider the following inequality:

$(3x)/(4)-1\text{ > }(x)/(3)-(3)/(5)$

Putting the similar terms together, we get:

$(3x)/(4)-\text{ }(x)/(3)\text{>}-(3)/(5)+1$

this is equivalent to:

this is equivalent to:

$(5x)/(12)\text{ >}(2)/(5)$

this is equivalent to:

$25x\text{ > 24}$

this is equivalent to:

$x>\text{ }(24)/(25)\text{ = 0.96}$

in interval notation, this is equivalent to:

$(0.96,\text{ }\infty)$

and the graph is:

Now, consider the following inequality:

$2x-(18)/(5)\text{ > }x+(2)/(5)$

Putting the similar terms together, we get:

$2x-x\text{ > }(2)/(5)+(18)/(5)$

this is equivalent to:

$x\text{ > }(20)/(5)=\text{ 4}$

in interval notation, this is equivalent to:

$(4,\infty)$

and the graph is:

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