Question 148484
Solve using addition and multiplication principals.
5 + 4x < 21
The solution set is {x/x ??} 



{{{5+4x<21}}} Start with the given inequality.



{{{4x<21-5}}} Subtract {{{5}}} from both sides.



{{{4x<16}}} Combine like terms on the right side.



{{{x<(16)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}. 



{{{x<4}}} Reduce.



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Answer:


So the answer is {{{x<4}}} 



So the solution set is  *[Tex \LARGE \left\{x\|x<4\right\}]



Which in interval notation is *[Tex \LARGE \left(-\infty,4\right)]


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Solve the following system of equation 

x + 4y = 2 (1)
x = 7 -4y (2)



Start with the given system

{{{x+4y=2}}}
{{{x=7-4y}}}




{{{7-4y+4y=2}}}  Plug in {{{x=7-4y}}} into the first equation. In other words, replace each {{{x}}} with {{{7-4y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{7=2}}} Combine like terms on the left side



{{{0=2-7}}}Subtract 7 from both sides



{{{0=-5}}} Combine like terms on the right side


Since this equation is <font size=4><b>never</b></font> true for any y value, this means there are no solutions.