The table shows the steps for solving the given inequality for x. −3(4 − 6x) < x + 5 select the reason for each step from the drop-down menus. –3(4 − 6x) < x + 5 given −12 + 18x < x + 5 −12 + 17x < 5 subtraction property of order 17 x < 17 x < 1

We are given :  -3(4-6x) < x+5.

Solution: -3 is in front of Parenthesis.

We need to multiply -3 by (4-6x).

So, we need to applying distributive property.

On distributing, we get

-12+18x < x+5        (By distributive property)

The reverse operation of addition is subtraction. So we need to subtract x from both sides, we get

-12+18x-x < x-x+5    (By subtraction property of equality).

-12+17x < 5

Now, we need to get rid -12 from left side.

So, we need to apply addition property of equality, we need to add 12 on both sides, we get

-12+12+18x < x+5+12    (By addition property of equality)

17x < 17

We need to get rid 17 from left side. So we need to apply division property of equality.

On dividing both sides by 17, we get

17x/17 < 17/17      (By division property of equality)

x < 1.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

answer: input the dimensions of the room to be painted. click the button to calculate the amount of paint and man-hours needed for this job.

interior paint coverage depends on the brand of paint used. the coverage amount is listed on the label of the paint can. use this to adjust the values in the paint coverage section below. paint usually is applied at 350 to 400 square feet per gallon (primer at 200 to 300 square feet per gallon).

step-by-step explanation: