Respuesta :

gmany

Answer:

[tex]\large\boxed{x<9\to x\in(-\infty,\ 9)}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{3}x+14-3x>-7\qquad\text{subtract 14 from both sides}\\\\\dfrac{2}{3}x+14-14-3x>-7-14\\\\\dfrac{2}{3}x-3x>-21\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x-(3)(3x)>(3)(-21)\\\\2x-9x>-63\\\\-7x>-63\qquad\text{change the signs}\\\\7x<63\qquad\text{divide both sides by 7}\\\\\dfrac{7x}{7}<\dfrac{63}{7}\\\\x<9[/tex]

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MathPhys

Answer:

x < 9

Step-by-step explanation:

[tex]\frac{2}{3} x+14-3x>-7[/tex]

First, write 3 as a fraction:

[tex]\frac{2}{3} x+14-\frac{3}{1}x>-7[/tex]

The common denominator is 3, so:

[tex]\frac{2}{3} x+14-\frac{9}{3}x>-7[/tex]

Combine the fractions:

[tex]\frac{2-9}{3} x+14>-7\\-\frac{7}{3} x+14>-7[/tex]

Subtract 14 from both sides:

[tex]-\frac{7}{3} x>-21[/tex]

Multiply both sides by 3:

[tex]-7x>-63[/tex]

Divide both sides by -7 (don't forget to flip the sign when multiplying or dividing by a negative number):

[tex]x<9[/tex]

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