# Khan/khan-exercises

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131 lines (123 sloc) 5.96 kB
 Absolute value equations
randRange( 2, 10 ) randRangeNonZero( -10, 10 ) randRange( 2, 10 ) randRangeNonZero( 2, 10 ) fractionReduce( D - B, A - C ) (function() { if ( ( D - B ) / ( A - C) > 0 ) { return "<code>" + "x = " + fractionReduce( -1 * abs( D - B ), abs( A - C ) ) + "\\text{ or }" + "x = " + fractionReduce( abs( D - B ), abs( A - C ) ) + "</code>"; } else { return "No solution"; } })() (function() { var choices = []; for ( var i = 0; i < 4; i++ ) { var choice = "<code>"; var nOffset = randRange( 1, 10 ); var dOffset = randRangeExclude( 1, 10, [ C - A ] ); if ( D - B + nOffset === 0 ) { choice += "x = 0"; } else { choice += "x = " + fractionReduce( -1 * abs( D - B + nOffset ), abs( A - C + dOffset ) ) + "\\text{ or }" + "x = " + fractionReduce( abs( D - B + nOffset ), abs( A - C + dOffset ) ); } choice += "</code>"; choices.unshift( choice ); } if ( ( D - B ) / ( A - C ) > 0 ) { choices.shift(); choices.unshift( SOLUTION ); choices = shuffle( choices ); choices.push( "No solution"); } else { choices = shuffle( choices ); choices.push( SOLUTION ); } return choices; })()

Solve for x:

A|x| + B = C|x| + D

SOLUTION

• choice

Subtract C|x| from both sides:

(A|x| + B) - C|x| = (C|x| + D) - C|x|

A - C|x| + B = D

B > 0 ? "Subtract" : "Add" abs(B) B > 0 ? "from" : "to" both sides:

(A - C|x| + B) + -B = D + -B

A - C|x| = D - B

Divide both sides by A - C.

\frac{A - C|x|}{A - C} = \frac{D - B}{A - C}

Simplify.

|x| = SIMPLIFIED

Subtract A|x| from both sides:

(A|x| + B) - A|x| = (C|x| + D) - A|x|

B = C - A|x| + D

D > 0 ? "Subtract" : "Add" abs(D) D > 0 ? "from" : "to" both sides:

B + -D = (C - A|x| + D) + -D

B - D = C - A|x|

Divide both sides by C - A.

\frac{B - D}{C - A} = \frac{C - A|x|}{C - A}

Simplify.

SIMPLIFIED = |x|

Thus, the correct answer is SOLUTION.

The absolute value cannot be negative. Therefore, there is no solution.

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