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# the product of the values of a for which |5a-4|=a is true is

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the product of the values of a for which |5a-4|=a is true is

Nov 11, 2017

#1
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Solve for a over the real numbers:
abs(5 a - 4) = a

Split the equation into two possible cases:
5 a - 4 = a or 5 a - 4 = -a

Subtract a - 4 from both sides:
4 a = 4 or 5 a - 4 = -a

Divide both sides by 4:
a = 1 or 5 a - 4 = -a

Add a + 4 to both sides:
a = 1 or 6 a = 4

Divide both sides by 6:
a = 1        or          a = 2/3     Their product is simply: 1 x 2/3 =2/3

Nov 11, 2017
edited by Guest  Nov 11, 2017

#1
0

Solve for a over the real numbers:
abs(5 a - 4) = a

Split the equation into two possible cases:
5 a - 4 = a or 5 a - 4 = -a

Subtract a - 4 from both sides:
4 a = 4 or 5 a - 4 = -a

Divide both sides by 4:
a = 1 or 5 a - 4 = -a

Add a + 4 to both sides:
a = 1 or 6 a = 4

Divide both sides by 6:
a = 1        or          a = 2/3     Their product is simply: 1 x 2/3 =2/3

Guest Nov 11, 2017
edited by Guest  Nov 11, 2017