document.write( "Question 24132: I cannot figure out how to do these two problems, I have tried it many different ways and cannot get the right answer. Help me! 1) |2(4-4x)+4|=3 and
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Algebra.Com's Answer #12824 by kev82(151)\"\" \"About 
You can put this solution on YOUR website!

I didn't learn how to solve these until university would you believe! They couldn't be easier once you know how to deal with them though.

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As I'm sure you know, the absolute value function gives you back it's argument without the sign. So if \"abs%28x%29=5\" then either \"x=5\" or \"-x=5\". Applying the same idea to your question 1, we get two equations:

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and

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Using the super automatic equation solver thingy, we get:

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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=1.125.
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  • Graphical form: Equation \"2%2A%284-4x%29%2B4=3\" was fully solved.
  • Text form: 2*(4-4x)+4=3 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+2%2A%284-4x%29%2B4=3+%29\"
    For tutors: simplify_cartoon( 2*(4-4x)+4=3 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"2%2A%28highlight_red%28+4+%29-4%2Ax%29%2B4=3\".
Moved \"4\" to the right of expression
It becomes \"2%2A%28-4%2Ax%2Bhighlight_green%28+4+%29%29%2B4=3\".
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Look at \"2%2A%28-4%2Ax%2B4%29%2B4=highlight_red%28+3+%29\".
Moved these terms to the left \"highlight_green%28+-3+%29\"
It becomes \"2%2A%28-4%2Ax%2B4%29%2B4-highlight_green%28+3+%29=0\".
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Look at \"2%2A%28-4%2Ax%2B4%29%2Bhighlight_red%28+4+%29-highlight_red%28+3+%29=0\".
Added fractions or integers together
It becomes \"2%2A%28-4%2Ax%2B4%29%2Bhighlight_green%28+1+%29=0\".
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Look at \"highlight_red%28+2%2A%28-4%2Ax%2B4%29+%29%2B1=0\".
Expanded term \"2\" by using associative property on \"%28-4%2Ax%2B4%29\"
It becomes \"-highlight_green%28+2%2A4%2Ax+%29%2Bhighlight_green%28+2%2A4+%29%2B1=0\".
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Look at \"-highlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2Ax%2B2%2A4%2B1=0\".
Multiplied numerator integers
It becomes \"-highlight_green%28+8+%29%2Ax%2B2%2A4%2B1=0\".
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Look at \"-8%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2B1=0\".
Multiplied numerator integers
It becomes \"-8%2Ax%2Bhighlight_green%28+8+%29%2B1=0\".
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Look at \"-8%2Ax%2Bhighlight_red%28+8+%29%2Bhighlight_red%28+1+%29=0\".
Added fractions or integers together
It becomes \"-8%2Ax%2Bhighlight_green%28+9+%29=0\".
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Look at \"highlight_red%28+-8%2Ax%2B9+%29=0\".
Solved linear equation \"highlight_red%28+-8%2Ax%2B9=0+%29\" equivalent to -8*x+9 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=1.125.

Universal Simplifier and Solver

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Done!

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and

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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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\n" ); document.write( "

\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


\n" ); document.write( "\n" ); document.write( "
    \n" ); document.write( "
  • This is an equation! Solutions: x=1.875.
    • \n" ); document.write( "
  • Graphical form: Equation \"-2%2A%284-4x%29-4=3\" was fully solved.
  • Text form: -2*(4-4x)-4=3 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+-2%2A%284-4x%29-4=3+%29\"
    For tutors: simplify_cartoon( -2*(4-4x)-4=3 )
    • \n" ); document.write( "
  • If you have a website, here's a link to this solution.
    • \n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "

DETAILED EXPLANATION

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Look at \"-2%2A%28highlight_red%28+4+%29-4%2Ax%29-4=3\".
Moved \"4\" to the right of expression
It becomes \"-2%2A%28-4%2Ax%2Bhighlight_green%28+4+%29%29-4=3\".
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Look at \"-2%2A%28-4%2Ax%2B4%29-4=highlight_red%28+3+%29\".
Moved these terms to the left \"highlight_green%28+-3+%29\"
It becomes \"-2%2A%28-4%2Ax%2B4%29-4-highlight_green%28+3+%29=0\".
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Look at \"-2%2A%28-4%2Ax%2B4%29-highlight_red%28+4+%29-highlight_red%28+3+%29=0\".
Added fractions or integers together
It becomes \"-2%2A%28-4%2Ax%2B4%29%2Bhighlight_green%28+-7+%29=0\".
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Look at \"-2%2A%28-4%2Ax%2B4%29%2Bhighlight_red%28+-7+%29=0\".
Removed extra sign in front of \"-7\"
It becomes \"-2%2A%28-4%2Ax%2B4%29-highlight_green%28+7+%29=0\".
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Look at \"-highlight_red%28+2%2A%28-4%2Ax%2B4%29+%29-7=0\".
Expanded term \"-2\" by using associative property on \"%28-4%2Ax%2B4%29\"
It becomes \"highlight_green%28+2%2A4%2Ax+%29-highlight_green%28+2%2A4+%29-7=0\".
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Look at \"highlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2Ax-2%2A4-7=0\".
Multiplied numerator integers
It becomes \"highlight_green%28+8+%29%2Ax-2%2A4-7=0\".
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Look at \"8%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+4+%29-7=0\".
Multiplied numerator integers
It becomes \"8%2Ax-highlight_green%28+8+%29-7=0\".
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Look at \"8%2Ax-highlight_red%28+8+%29-highlight_red%28+7+%29=0\".
Added fractions or integers together
It becomes \"8%2Ax%2Bhighlight_green%28+-15+%29=0\".
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Look at \"8%2Ax%2Bhighlight_red%28+-15+%29=0\".
Removed extra sign in front of \"-15\"
It becomes \"8%2Ax-highlight_green%28+15+%29=0\".
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Look at \"highlight_red%28+8%2Ax-15+%29=0\".
Solved linear equation \"highlight_red%28+8%2Ax-15=0+%29\" equivalent to 8*x-15 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=1.875.

Universal Simplifier and Solver

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Done!

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Don't forget to put your answers back in to check!

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Now you know how to do the first problem, have another go at the second one again yourself, but don't forget the really imporant rule:

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When you multiply an inequality by a negative number you must reverse the sign.

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I've forgotton to do that far too many times

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Hope that helps

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Kev

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