Solve the following inequality

Question

Solve the following inequality:

(-7/8x) > (-3/16)

Answer 1

-7x/8 > -3/16 multiply by -16, which reverses the inequality sign

14x < 3 divide by 14

x < 3/14

check the solution. plug 3/14 for x

(-7/8)3/14) = -3/16

-3/16 = -3/16

then try a number less than 3/14, such as 0

-7(0)/8 > -3/16

0 > -3/16

It works. zero is greater than any negative number

UNLESS you meant

-7/8x > -3/16 Multiply by -16x

14 < 3x

3x > 14 divide by 3

x > 14/3

x > 4 2/3

check the answer

-7/8(14/3) = -3/16

-7/8)(3/14) = -3/16

-3/16 =-3/16

try a number larger than 14/3 such as 5

-7/8(5) > -3/15

-7/40 > -3/15 Put them over a common denominator, 120

-21/120 > -24/120 multiply by 120

-21 > -24 multiply by -1 and reverse the inequality

21 < 24

It works

x > or = 14/3

Answer 2

Solution:

(-7/8x) > (-3/16) Cross multiply you get (-3)(8x) ≤≤ (-7)(16) , -24x ≤ -112 Multiply by -1 note when you multiply by -1 the inequality sign gets reversed and you get 24x ≥ 112 simplify you get 6x ≥ 28 , and x ≥ 28/6, x ≥ 14/3 or

x ≥ 4.666 in decimals