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the inequality 7 - 2/3x < x - 8 is equivalent to

1) x > 9
2) x > -3/5
3) x < 9
4) x < -3/5

and how is that so? thank you x

Verified Answer :

welshfella

the rules are similar to those for equations
first add 2/3 x to both sides
7 < x + 2/3 x - 8
add 8 to both sides
15 < 5/3 x
inverting we get
5/3 x > 15 
now divide both sides by 5/3
x >  15 / 5/3 = 15 * 3/5 =  9

x > 9

The inequality \(7 - 2\div 3x < x - 8\) is equivalent to x>9.

  • The calculation is as follows;

Here we need to add 2 by 3 x to both sides

\(7 < x + 2\div 3 x - 8\)

add 8 to both sides

\(15 < 5\div 3 x\)

inverting we get

\(5\div 3 x > 15\)

now divide both sides by 5/3

\(x > 15 \div 5\div 3 = 15 \times 3\div 5 = 9\)


x > 9

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