Answer:
[tex]x = 1[/tex]
Step-by-step explanation:
Given
[tex]|\frac{1}{3} - \frac{x}{4}| = \frac{7}{12}[/tex]
Required
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Take LCM
[tex]|\frac{4 - 3x}{12}| = \frac{7}{12}[/tex]
Rewrite as:
[tex]\frac{1}{12}|4 - 3x| = \frac{7}{12}[/tex]
Multiply through by 12, we have:
[tex]|4 - 3x| = 7[/tex]
Remove the sign of absolute value
[tex]4 - 3x = 7[/tex] or [tex]4 - 3x = -7[/tex]
[tex]-3x = 7 - 4[/tex] or [tex]-3x = 4 - 7[/tex]
[tex]-3x = 11[/tex] or [tex]-3x = -3[/tex]
[tex]x = \frac{-11}{3}[/tex] or [tex]x = 1[/tex]
Since x is an integer, then:
[tex]x = 1[/tex]
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