Question 146193
First let's solve {{{5x+3>=-37}}}




{{{5x+3>=-37}}} Start with the given inequality.



{{{5x>=-37-3}}} Subtract {{{3}}} from both sides.



{{{5x>=-40}}} Combine like terms on the right side.



{{{x>=(-40)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}. 



{{{x>=-8}}} Reduce.



So the first part of our answer is {{{x>=-8}}}




Here's the graph of the first solution set


{{{drawing(500,80,-18, 2,-10, 10,
number_line( 500, -18, 2),

arrow(-8,0,2,0),
arrow(-8,0.30,2,0.30),
arrow(-8,0.15,2,0.15),
arrow(-8,-0.15,2,-0.15),
arrow(-8,-0.30,2,-0.30),

circle(-8,0,0.2),
circle(-8,0,0.15),
circle(-8,0,0.1),
circle(-8,0,0.2-0.02)
)}}}




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Now let's solve {{{4x+4>=-8}}}





{{{4x+4>=-8}}} Start with the given inequality.



{{{4x>=-8-4}}} Subtract {{{4}}} from both sides.



{{{4x>=-12}}} Combine like terms on the right side.



{{{x>=(-12)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}. 



{{{x>=-3}}} Reduce.



So the second part of our answer is {{{x>=-3}}}




Here's the graph of the second solution set


{{{drawing(500,80,-13, 7,-10, 10,
number_line( 500, -13, 7),

arrow(-3,0,7,0),
arrow(-3,0.30,7,0.30),
arrow(-3,0.15,7,0.15),
arrow(-3,-0.15,7,-0.15),
arrow(-3,-0.30,7,-0.30),

circle(-3,0,0.2),
circle(-3,0,0.15),
circle(-3,0,0.1),
circle(-3,0,0.2-0.02)
)}}}





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---------------------- Summary ----------------------



So together our answers are


{{{x>=-8}}} or {{{x>=-3}}}



and their combined graphs make


{{{drawing(500,80,-18, 2,-10, 10,
number_line( 500, -18, 2),

arrow(-8,0,2,0),
arrow(-8,0.30,2,0.30),
arrow(-8,0.15,2,0.15),
arrow(-8,-0.15,2,-0.15),
arrow(-8,-0.30,2,-0.30),

circle(-8,0,0.2),
circle(-8,0,0.15),
circle(-8,0,0.1),
circle(-8,0,0.2-0.02)
)}}}