SOLUTION: 5)3(x+4)=2(x+6)+x what is the solution set? 10)2|4t-5|+|4t-5|=45 what does t equal? 11)(t+3)^2+12=98 what does t equal? 12)5y^2+19y-45=5y(y+2) what does y equal? a

Algebra ->  Equations -> SOLUTION: 5)3(x+4)=2(x+6)+x what is the solution set? 10)2|4t-5|+|4t-5|=45 what does t equal? 11)(t+3)^2+12=98 what does t equal? 12)5y^2+19y-45=5y(y+2) what does y equal? a      Log On


   

Question 171352This question is from textbook algebra 1
: 5)3(x+4)=2(x+6)+x
what is the solution set?
10)2|4t-5|+|4t-5|=45
what does t equal?
11)(t+3)^2+12=98
what does t equal?
12)5y^2+19y-45=5y(y+2)
what does y equal?
and then problems 14, 15, and 16 that are also on page 196 in the chapter 4 chapter test. we have a test tommorrow and i wanna make sure my answers are right. thank you so much.
This question is from textbook algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'll do the first three to help you get started.


# 5


3%28x%2B4%29=2%28x%2B6%29%2Bx Start with the given equation.


3x%2B12=2x%2B12%2Bx Distribute.


3x%2B12=3x%2B12 Combine like terms on the right side.


3x=3x%2B12-12 Subtract 12 from both sides.


3x-3x=12-12 Subtract 3x from both sides.


0x=12-12 Combine like terms on the left side.


0x=0 Combine like terms on the right side.


0=0 Simplify.


Since this equation is ALWAYS true for any x value, this means x can equal any number. So there are an infinite number of solutions.






# 10


2%2Aabs%284t-5%29%2Babs%284t-5%29=45 Start with the given equation


Let z=abs%284t-5%29


2z%2Bz=45 Replace each abs%284t-5%29 with "z".


3z=45 Combine like terms on the left side.


z=%2845%29%2F%283%29 Divide both sides by 3 to isolate z.


z=15 Reduce.


abs%284t-5%29=15 Plug in z=abs%284t-5%29


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

4t-5=-15 or 4t-5=15 Set the expression 4t-5 equal to the original value 15 and it's opposite -15




Now lets focus on the first equation 4t-5=-15


4t=-15%2B5Add 5 to both sides


4t=-10 Combine like terms on the right side


t=%28-10%29%2F%284%29 Divide both sides by 4 to isolate t


t=-5%2F2 Reduce


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Now lets focus on the second equation 4t-5=15



4t=15%2B5Add 5 to both sides


4t=20 Combine like terms on the right side


t=%2820%29%2F%284%29 Divide both sides by 4 to isolate t



t=5 Divide



So the solutions are:

t=-5%2F2 or t=5





# 11


%28t%2B3%29%5E2%2B12=98 Start with the given equation.


%28t%2B3%29%5E2=98-12Subtract 12 from both sides.


%28t%2B3%29%5E2=86 Combine like terms.


x%2B3=0%2B-sqrt%2886%29 Take the square root of both sides.


t%2B3=sqrt%2886%29 or t%2B3=-sqrt%2886%29 Break up the "plus/minus" to form two equations.


t=-3%2Bsqrt%2886%29 or t=-3-sqrt%2886%29 Subtract 3 from both sides.


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Answer:


So the solutions are t=-3%2Bsqrt%2886%29 or t=-3-sqrt%2886%29.