SOLUTION: Solve and check. Label any contradictions or identities. 5(t+1)+8=3(t-2)+6

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Question 586648: Solve and check. Label any contradictions or identities.
5(t+1)+8=3(t-2)+6
Answer by eschwartz(9) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: t=-6.5.
  • Graphical form: Equation 5%2A%28t%2B1%29%2B8=3%2A%28t-2%29%2B6 was fully solved.
  • Text form: 5*(t+1)+8=3*(t-2)+6 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2A%28t%2B1%29%2B8=3%2A%28t-2%29%2B6+%29
    For tutors: simplify_cartoon( 5*(t+1)+8=3*(t-2)+6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2A%28t%2B1%29%2B8=highlight_red%28+3%2A%28t-2%29%2B6+%29.
Moved these terms to the left highlight_green%28+-3%2A%28t-2%29+%29,highlight_green%28+-6+%29
It becomes 5%2A%28t%2B1%29%2B8-highlight_green%28+3%2A%28t-2%29+%29-highlight_green%28+6+%29=0.
Look at 5%2A%28t%2B1%29%2Bhighlight_red%28+8+%29-3%2A%28t-2%29-highlight_red%28+6+%29=0.
Added fractions or integers together
It becomes 5%2A%28t%2B1%29%2Bhighlight_green%28+2+%29-3%2A%28t-2%29=0.
Look at 5%2A%28t%2B1%29%2Bhighlight_red%28+2+%29-3%2A%28t-2%29=0.
Moved 2 to the right of expression
It becomes 5%2A%28t%2B1%29-3%2A%28t-2%29%2Bhighlight_green%28+2+%29=0.
Look at highlight_red%28+5%2A%28t%2B1%29+%29-3%2A%28t-2%29%2B2=0.
Expanded term 5 by using associative property on %28t%2B1%29
It becomes highlight_green%28+5%2At+%29%2Bhighlight_green%28+5%2A1+%29-3%2A%28t-2%29%2B2=0.
Look at 5%2At%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+1+%29-3%2A%28t-2%29%2B2=0.
Multiplied numerator integers
It becomes 5%2At%2Bhighlight_green%28+5+%29-3%2A%28t-2%29%2B2=0.
Look at 5%2At%2Bhighlight_red%28+5+%29-3%2A%28t-2%29%2Bhighlight_red%28+2+%29=0.
Added fractions or integers together
It becomes 5%2At%2Bhighlight_green%28+7+%29-3%2A%28t-2%29=0.
Look at 5%2At%2Bhighlight_red%28+7+%29-3%2A%28t-2%29=0.
Moved 7 to the right of expression
It becomes 5%2At-3%2A%28t-2%29%2Bhighlight_green%28+7+%29=0.
Look at 5%2At-highlight_red%28+3%2A%28t-2%29+%29%2B7=0.
Expanded term -3 by using associative property on %28t-2%29
It becomes 5%2At-highlight_green%28+3%2At+%29%2Bhighlight_green%28+3%2A2+%29%2B7=0.
Look at 5%2At-3%2At%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29%2B7=0.
Multiplied numerator integers
It becomes 5%2At-3%2At%2Bhighlight_green%28+6+%29%2B7=0.
Look at 5%2At-3%2At%2Bhighlight_red%28+6+%29%2Bhighlight_red%28+7+%29=0.
Added fractions or integers together
It becomes 5%2At-3%2At%2Bhighlight_green%28+13+%29=0.
Look at highlight_red%28+5%2At+%29-highlight_red%28+3%2At+%29%2B13=0.
Eliminated similar terms highlight_red%28+5%2At+%29,highlight_red%28+-3%2At+%29 replacing them with highlight_green%28+%285-3%29%2At+%29
It becomes highlight_green%28+%285-3%29%2At+%29%2B13=0.
Look at %28highlight_red%28+5+%29-highlight_red%28+3+%29%29%2At%2B13=0.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2At%2B13=0.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2At+%29%2B13=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2At%2B13=0.
Look at highlight_red%28+2%2At%2B13+%29=0.
Solved linear equation highlight_red%28+2%2At%2B13=0+%29 equivalent to 2*t+13 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=-6.5.

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Done!