Question

cuanto es x + 8 > 3x - 4, 2x – 1 > 4x + 2, 9x + 8 > 2x - 5?

Answer 1

Respuesta:

x+3>2x+1 : [ Solution: x<

2

3 Decimal: x<0.66666… Interval Notation: (−∞ ,

2

3 ) ]

Pasos

$-x+3>2x+1$−x+3>2x+1

$\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}$Subtract 3 from both sides

$-x+3-3>2x+1-3$−x+3−3>2x+1−3

$\mathrm{Simplify}$Simplify

$-x>2x-2$−x>2x−2

$\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}$Subtract 2x from both sides

$-x-2x>2x-2-2x$−x−2x>2x−2−2x

$\mathrm{Simplify}$Simplify

$-3x>-2$−3x>−2

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$Multiply both sides by −1 (reverse the inequality)

$\left(-3x\right)\left(-1\right)<\left(-2\right)\left(-1\right)$(−3x)(−1)<(−2)(−1)

$\mathrm{Simplify}$Simplify

$3x<2$3x<2

$\mathrm{Divide\:both\:sides\:by\:}3$Divide both sides by 3

$\frac{3x}{3}<\frac{2}{3}$

3x

3 <

2

3

$\mathrm{Simplify}$Simplify

$x<\frac{2}{3}$x<

2

3