SOLUTION: Eight less than the product of -3 and a number is greater than -26.find the values of the number

Question 1190454: Eight less than the product of -3 and a number is greater than -26.find the values of the number

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your answer should be x < 6

when x = 5, -3x - 8 = -15 - 8 = -23 which is greater than -26.
when x = 6, -3x - 8 = -18 - 8 = -26 which is equal to -26.
when x = 7, -3x - 8 = -21 - 8 = -29 which is less than -26.

the solution is that x < 6.

it was solved in the following manner.

start with -3x - 8 > -26
x represents the number.
add 8 to both sides to get -3x > -18
divide both sides by -3 to get x < 6
dividing both sides by a negative number reverses the inequality.
x < 6 is your solution.

let me know if you have any questions.
theo
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Eight less than the product of -3 and a number is greater than -26.

Translate into an equation:
"Eight less than..." --> ____ -8
"Eight less than the product of -3 and a number..." --> -3x-8
"Eight less than the product of -3 and a number is greater than -26" --> -3x-8>-26

The other tutor does what nearly everybody else does -- leave the x term on the left. That leads to solving the inequality by dividing both sides by a negative number, which switches the direction of the inequality. No matter how experienced you are, it is easy to forget to change the direction when dividing by a negative.

So avoid having to divide by a negative by rearranging the inequality so the sign on the x term is positive:

-3x-8>-26
-8>3x-26
18>3x
6>x --> x<6

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