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.
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:
