8 less than the product of - 3 and anumber is greater than - 26.

8 less than means - 8

product of means multiplication of some things

product of - 3 and a number means - 3 times a number

is greater than means >

-26 so

-8+-3 times a number>-26

solve for 'a number'

add 8 to both sides

-3 times a number>-18

divide both sides by - 3

remember tha twhen you divide or multiply by a negative, the inequality sign flips

a number<6

so the number is less than 6

The inequality expression would be: - 3x - 8 > - 26

-3x - 8 > - 26

+ 8 + 8

-3x > - 18

: - 3 : - 3

x > 6 ⇒ becomes x < 6

Notice the change in the inequality sign? This flip is done when the division and multiplication is made by a negative number. In this case, - 3 is the divisor.

It is generally done during the first part of the inequality. However, to avoid confusion, flipping the inequality sign is done at the end of the solution.

Assuming: x = 5

-3 (5) - 8 > - 26

-15 - 8 > - 26

-23 > - 26