SOLUTION: Solve and check the linear equations 3[-3x + 4 - 7(x+1)] = 2x + 5

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Question 21695: Solve and check the linear equations
3[-3x + 4 - 7(x+1)] = 2x + 5
Answer by Alwayscheerful(414) 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: x=-0.4375.
  • Graphical form: Equation 3%2A%28-3x%2B4-7%2A%28x%2B1%29%29=2x%2B5 was fully solved.
  • Text form: 3*(-3x+4-7*(x+1))=2x+5 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3%2A%28-3x%2B4-7%2A%28x%2B1%29%29=2x%2B5+%29
    For tutors: simplify_cartoon( 3*(-3x+4-7*(x+1))=2x+5 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2A%28-3%2Ax%2Bhighlight_red%28+4+%29-7%2A%28x%2B1%29%29=2x%2B5.
Moved 4 to the right of expression
It becomes 3%2A%28-3%2Ax-7%2A%28x%2B1%29%2Bhighlight_green%28+4+%29%29=2x%2B5.
Look at 3%2A%28-3%2Ax-7%2A%28x%2B1%29%2B4%29=highlight_red%28+2%2Ax%2B5+%29.
Moved these terms to the left highlight_green%28+-2%2Ax+%29,highlight_green%28+-5+%29
It becomes 3%2A%28-3%2Ax-7%2A%28x%2B1%29%2B4%29-highlight_green%28+2%2Ax+%29-highlight_green%28+5+%29=0.
Look at highlight_red%28+3%2A%28-3%2Ax-7%2A%28x%2B1%29%2B4%29+%29-2%2Ax-5=0.
Expanded term 3 by using associative property on %28-3%2Ax-7%2A%28x%2B1%29%2B4%29
It becomes .
Look at -highlight_red%28+3+%29%2Ahighlight_red%28+3+%29%2Ax-3%2A7%2A%28x%2B1%29%2B3%2A4-2%2Ax-5=0.
Multiplied numerator integers
It becomes -highlight_green%28+9+%29%2Ax-3%2A7%2A%28x%2B1%29%2B3%2A4-2%2Ax-5=0.
Look at -9%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+7+%29%2A%28x%2B1%29%2B3%2A4-2%2Ax-5=0.
Multiplied numerator integers
It becomes -9%2Ax-highlight_green%28+21+%29%2A%28x%2B1%29%2B3%2A4-2%2Ax-5=0.
Look at -9%2Ax-21%2A%28x%2B1%29%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+4+%29-2%2Ax-5=0.
Multiplied numerator integers
It becomes -9%2Ax-21%2A%28x%2B1%29%2Bhighlight_green%28+12+%29-2%2Ax-5=0.
Look at -9%2Ax-21%2A%28x%2B1%29%2Bhighlight_red%28+12+%29-2%2Ax-highlight_red%28+5+%29=0.
Added fractions or integers together
It becomes -9%2Ax-21%2A%28x%2B1%29%2Bhighlight_green%28+7+%29-2%2Ax=0.
Look at -9%2Ax-21%2A%28x%2B1%29%2Bhighlight_red%28+7+%29-2%2Ax=0.
Moved 7 to the right of expression
It becomes -9%2Ax-21%2A%28x%2B1%29-2%2Ax%2Bhighlight_green%28+7+%29=0.
Look at -highlight_red%28+9%2Ax+%29-21%2A%28x%2B1%29-highlight_red%28+2%2Ax+%29%2B7=0.
Eliminated similar terms highlight_red%28+-9%2Ax+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%28-9-2%29%2Ax+%29
It becomes highlight_green%28+%28-9-2%29%2Ax+%29-21%2A%28x%2B1%29%2B7=0.
Look at %28-highlight_red%28+9+%29-highlight_red%28+2+%29%29%2Ax-21%2A%28x%2B1%29%2B7=0.
Added fractions or integers together
It becomes %28highlight_green%28+-11+%29%29%2Ax-21%2A%28x%2B1%29%2B7=0.
Look at %28highlight_red%28+-11+%29%29%2Ax-21%2A%28x%2B1%29%2B7=0.
Removed extra sign in front of -11
It becomes %28-highlight_green%28+11+%29%29%2Ax-21%2A%28x%2B1%29%2B7=0.
Look at highlight_red%28+%28-highlight_red%28+11+%29%29%2Ax+%29-21%2A%28x%2B1%29%2B7=0.
Remove unneeded parentheses around factor highlight_red%28+11+%29
It becomes -highlight_green%28+11+%29%2Ax-21%2A%28x%2B1%29%2B7=0.
Look at -11%2Ax-highlight_red%28+21%2A%28x%2B1%29+%29%2B7=0.
Expanded term -21 by using associative property on %28x%2B1%29
It becomes -11%2Ax-highlight_green%28+21%2Ax+%29-highlight_green%28+21%2A1+%29%2B7=0.
Look at -11%2Ax-21%2Ax-highlight_red%28+21+%29%2Ahighlight_red%28+1+%29%2B7=0.
Multiplied numerator integers
It becomes -11%2Ax-21%2Ax-highlight_green%28+21+%29%2B7=0.
Look at -11%2Ax-21%2Ax-highlight_red%28+21+%29%2Bhighlight_red%28+7+%29=0.
Added fractions or integers together
It becomes -11%2Ax-21%2Ax%2Bhighlight_green%28+-14+%29=0.
Look at -11%2Ax-21%2Ax%2Bhighlight_red%28+-14+%29=0.
Removed extra sign in front of -14
It becomes -11%2Ax-21%2Ax-highlight_green%28+14+%29=0.
Look at -highlight_red%28+11%2Ax+%29-highlight_red%28+21%2Ax+%29-14=0.
Eliminated similar terms highlight_red%28+-11%2Ax+%29,highlight_red%28+-21%2Ax+%29 replacing them with highlight_green%28+%28-11-21%29%2Ax+%29
It becomes highlight_green%28+%28-11-21%29%2Ax+%29-14=0.
Look at %28-highlight_red%28+11+%29-highlight_red%28+21+%29%29%2Ax-14=0.
Added fractions or integers together
It becomes %28highlight_green%28+-32+%29%29%2Ax-14=0.
Look at %28highlight_red%28+-32+%29%29%2Ax-14=0.
Removed extra sign in front of -32
It becomes %28-highlight_green%28+32+%29%29%2Ax-14=0.
Look at highlight_red%28+%28-highlight_red%28+32+%29%29%2Ax+%29-14=0.
Remove unneeded parentheses around factor highlight_red%28+32+%29
It becomes -highlight_green%28+32+%29%2Ax-14=0.
Look at highlight_red%28+-32%2Ax-14+%29=0.
Solved linear equation highlight_red%28+-32%2Ax-14=0+%29 equivalent to -32*x-14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-0.4375.

Universal Simplifier and Solver


Done!

Hope this helps!