Solve |1/3x + 5| = |3/4x − 2|.

Answer 1

Given: abs[ (1/3)x + 5 ] = abs[ (3/4)x - 2 ]

Note: Original problem statement

is not clear regarding coefficients of x.

**** SOLUTION:

(1/3)x + 5 = +/- [ (3/4)x - 2 ]

(1/3)x = -5 +/- [ (3/4)x - 2 ]

x = -15 +/- 3[(3/4)x - 2]

x = -15 +/- [(9/4)x - 4]

x = -15 + (9/4)x - 6 OR x = -15 - (9/4)x + 6

-(5/4)x = -21 OR (13/4)x = -9

x = 84/5 OR x = -36/13

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CHECK: x = 84/5

abs[ (1/3)x + 5 ] = abs[ (3/4)x - 2 ]

abs[ (1/3)(84/5) + 5 ] = abs[ (3/4)(84/5) - 2 ]

abs[ (53/5 ] = abs[ 53/5 ] YES!

CHECK: x = -36/13

abs[ (1/3)x + 5 ] = abs[ (3/4)x - 2 ]

abs[ (1/3)(-36/13) + 5 ] = abs[ (3/4)(-36/13) - 2 ]

abs[ (53/13 ] = abs[ 53/13 ] YES!

Answer 2

(1/3)x + 5 = (3/4)x - 2 or (1/3) x + 5 = 2 - (3/4)x-2

(1/3)x + 5 = (3/4)x - 2

multiplies both sides by 12:

4x + 60 = 9x - 24

60 = 5x - 24

84 = 5x

84/5 = x

check:

(1/3)(84/5) + 5 =

84/15 + 75/15 =

159/15

(3/4)(84/5) - 2 =

(3/1)(21/5) - 2 =

63/5 - 2 =

63/5 - 10/5 = 55/5 = 11

does not check out

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(1/3) x + 5 = 2 - (3/4)x

4x + 60 = 24 - 9x

13x + 60 = 24

13x = -36

x = -36/13

check:

(1/3)(-36/13) + 5 =

(-12/13) + 5 =

(-12/13) + 65/13 =

53/13

2 - (3/4)(-36/13) =

2 - (3* -9)/13 =

2 - (-27/13) =

26/13 - -27/13 =

53/13

this solution checks