Question 168182
# 1


To see if any values are solutions, we need to test them all




Let's see if {{{y=7}}} is a solution.



{{{y-10>2y-3}}} Start with the given inequality.



{{{7-10>2*(7)-3}}} Plug in {{{y=7}}}.



{{{7-10>14-3}}} Multiply



{{{-3>11}}} Combine like terms.



Since the inequality {{{-3>11}}} is <font size="4"><b>FALSE</b></font>,this means that {{{y=7}}} is <font size="4"><b>NOT</b></font> a solution.



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Let's see if {{{y=-18}}} is a solution.



{{{y-10>2y-3}}} Start with the given inequality.



{{{-18-10>2*(-18)-3}}} Plug in {{{y=-18}}}.



{{{-18-10>-36-3}}} Multiply



{{{-28>-39}}} Combine like terms.



Since the inequality {{{-3>11}}} is <font size="4"><b>TRUE</b></font>,this means that {{{y=-18}}} is a solution to the inequality.



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Let's see if {{{y=-11}}} is a solution.



{{{y-10>2y-3}}} Start with the given inequality.



{{{-11-10>2*(-11)-3}}} Plug in {{{y=-11}}}.



{{{-11-10>-22-3}}} Multiply



{{{-21>-25}}} Combine like terms.



Since the inequality {{{-21>-25}}} is <font size="4"><b>TRUE</b></font>,this means that {{{y=-11}}} is a solution to the inequality.



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Finally, let's see if {{{y=-3}}} is a solution.



{{{y-10>2y-3}}} Start with the given inequality.



{{{-3-10>2*(-3)-3}}} Plug in {{{y=-11}}}.



{{{-3-10>-6-3}}} Multiply



{{{-13>-9}}} Combine like terms.



Since the inequality {{{-21>-25}}} is <font size="4"><b>FALSE</b></font>,this means that {{{y=-11}}} is <font size="4"><b>NOT</b></font> a solution to the inequality.



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Answer:



So the solutions of the inequality are {{{y=-18}}} and {{{y=-11}}}.





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# 2



*[Tex \LARGE \left\{x\|x \ge -5\right\}] written in interval notation is <font size="8">[</font>*[Tex \LARGE -5,\infty]<font size="8">)</font>



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# 3



First rewrite -5 > x > -7 into -7 < x < -5



So the answer in interval notation is 



<font size="8">(</font>*[Tex \LARGE \bf{-7,-5}]<font size="8">)</font>




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# 4  





{{{-(7/2)x>-5/4}}} Start with the given inequality.



{{{4(-(7/cross(2))x)>cross(4)(-5/cross(4))}}} Multiply both sides by the LCD {{{4}}} to clear the fractions.



{{{-14x>-5}}} Distribute and multiply.



{{{x<(-5)/(-14)}}} Divide both sides by {{{-14}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<5/14}}} Reduce.



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Answer:


So the answer is {{{x<5/14}}} 



Which approximates to {{{x<0.357}}} 




So the solution set is  *[Tex \LARGE \left\{x\|x<\frac{5}{14}\right\}]