document.write( "Question 21695: Solve and check the linear equations
\n" ); document.write( "3[-3x + 4 - 7(x+1)] = 2x + 5 \n" ); document.write( "

Algebra.Com's Answer #10489 by Alwayscheerful(414) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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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.

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DETAILED EXPLANATION

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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 $\"3%2A%28-3%2Ax-7%2A%28x%2B1%29%2Bhighlight_green%28+4+%29%29=2x%2B5\"$ .
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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 $\"3%2A%28-3%2Ax-7%2A%28x%2B1%29%2B4%29-highlight_green%28+2%2Ax+%29-highlight_green%28+5+%29=0\"$ .
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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

.
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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 $\"-highlight_green%28+9+%29%2Ax-3%2A7%2A%28x%2B1%29%2B3%2A4-2%2Ax-5=0\"$ .
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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 $\"-9%2Ax-highlight_green%28+21+%29%2A%28x%2B1%29%2B3%2A4-2%2Ax-5=0\"$ .
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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 $\"-9%2Ax-21%2A%28x%2B1%29%2Bhighlight_green%28+12+%29-2%2Ax-5=0\"$ .
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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 $\"-9%2Ax-21%2A%28x%2B1%29%2Bhighlight_green%28+7+%29-2%2Ax=0\"$ .
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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 $\"-9%2Ax-21%2A%28x%2B1%29-2%2Ax%2Bhighlight_green%28+7+%29=0\"$ .
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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 $\"highlight_green%28+%28-9-2%29%2Ax+%29-21%2A%28x%2B1%29%2B7=0\"$ .
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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 $\"%28highlight_green%28+-11+%29%29%2Ax-21%2A%28x%2B1%29%2B7=0\"$ .
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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 $\"%28-highlight_green%28+11+%29%29%2Ax-21%2A%28x%2B1%29%2B7=0\"$ .
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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 $\"-highlight_green%28+11+%29%2Ax-21%2A%28x%2B1%29%2B7=0\"$ .
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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 $\"-11%2Ax-highlight_green%28+21%2Ax+%29-highlight_green%28+21%2A1+%29%2B7=0\"$ .
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Look at $\"-11%2Ax-21%2Ax-highlight_red%28+21+%29%2Ahighlight_red%28+1+%29%2B7=0\"$ .
Multiplied numerator integers
It becomes $\"-11%2Ax-21%2Ax-highlight_green%28+21+%29%2B7=0\"$ .
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Look at $\"-11%2Ax-21%2Ax-highlight_red%28+21+%29%2Bhighlight_red%28+7+%29=0\"$ .
Added fractions or integers together
It becomes $\"-11%2Ax-21%2Ax%2Bhighlight_green%28+-14+%29=0\"$ .
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Look at $\"-11%2Ax-21%2Ax%2Bhighlight_red%28+-14+%29=0\"$ .
Removed extra sign in front of $\"-14\"$
It becomes $\"-11%2Ax-21%2Ax-highlight_green%28+14+%29=0\"$ .
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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 $\"highlight_green%28+%28-11-21%29%2Ax+%29-14=0\"$ .
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Look at $\"%28-highlight_red%28+11+%29-highlight_red%28+21+%29%29%2Ax-14=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-32+%29%29%2Ax-14=0\"$ .
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Look at $\"%28highlight_red%28+-32+%29%29%2Ax-14=0\"$ .
Removed extra sign in front of $\"-32\"$
It becomes $\"%28-highlight_green%28+32+%29%29%2Ax-14=0\"$ .
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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 $\"-highlight_green%28+32+%29%2Ax-14=0\"$ .
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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: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=-0.4375.

Universal Simplifier and Solver

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Done!

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