Respuesta :

itzshahrad

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

First simplify the equation.

  1. [tex]\frac{7}{9}x -\frac{4}{9} =\frac{1}{4} +\frac{5}{12}[/tex]
  2. [tex]\frac{3}{9}x= \frac{3}{12} +\frac{5}{12}[/tex]
  3. [tex]\frac{3}{9}x=\frac{8}{12}[/tex]
  4. [tex]\frac{1}{3}x=\frac{2}{3}[/tex]

Now multiply both sides by 3.

[tex]x = 2[/tex]

I hope it helps you. Please choose my answer as the BRAINLIEST.

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

[tex]\cfrac{7}{9}\:x-\cfrac{4}{9}\:x=\cfrac{1}{4}+\cfrac{5}{12}[/tex]

First, combine  [tex]\frac{7}{9} x[/tex] and [tex]-\frac{4}{9} x[/tex] =  [tex]\frac{1}{3} x[/tex]

[tex]\cfrac{1}{3}\: x=\cfrac{1}{4} +\cfrac{5}{12}[/tex]

LCM of 4 and 12 is 12, Convert 1/4 and 5/12 to fraction with denominator 12:

[tex]\cfrac{1}{3}\: x=\cfrac{3}{12} +\cfrac{5}{12}[/tex]

Since 3/12 and 5/12 have the same denominator, let's add numerators:

[tex]\cfrac{1}{3}\:x=\cfrac{3+5}{12}[/tex]

[tex]\cfrac{1}{3}\:x=\cfrac{8}{12}[/tex]

Reduce the fraction 8/12 to lowest term by extracting and  canceling out 4,

[tex]\cfrac{1}{3} \:x=\cfrac{2}{3}[/tex]

Multiply both sides by 3, reciprocal of 1/3:

[tex]x=\cfrac{2}{3} \times 3[/tex]

Cancel out 3 and 3:

[tex]x=2[/tex]

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