the product of 6 and the difference of 6x and 3 is less than or equal to the product of -2 and the sum of 4 and 8x

Answer 1

"the product of 6 and": we will be multiplying 6 and whatever comes after this phrase.

"the difference of 6x and 3": this translates to the subtraction of 6x and 3 or (6x - 3).

So, it's the PRODUCT OF 6 & (6x - 3), which looks like this.... 6(6x - 3)

"is less than or equal to": indicates that the inequality sign will be the less than or equal to sign (≤)

"the product of -2 and": we will be multiplying the number -2 by whatever comes after this phrase.

"the sum of 4 and 8x": means to add together 4 and 8x --- (4 + 8x)

We will multiply (4 + 8x) buy the number -2

-2(4 + 8x)

Therefore the first algebraic expression [6(6x - 3)] is going to be less than or equal to (≤) the second algebraic expression [-2(4 + 8x)]

6(6x - 3) ≤ -2(4 + 8x)

Answer 2

The key to this problem is translating the words into numerical expressions:

"Product" means multiplication and "difference" means subtraction, so the product of 6 and the difference of 6x and 3 can be written as: 6(6x - 3). "Sum" means addition, so the product of -2 and the sum of 4 and 8x can be written as -2(4 + 8x).

When we add in the less than or equal to sign, we get: 6(6x - 3) ≤ -2(4 + 8x)

Using the Distributive Property on the left side, we multiply the 6 on the outside by the 6x and the -3 in the parentheses to get: 36x - 18.

Using the Distributive Property on the right side, we multiply the -2 on the outside by the 4 and the 8x in the parentheses to get: -8 - 16x.

36x - 18 ≤ -8 - 16x

Add 18 to both sides: 36x ≤ 10 - 16x

Add 16x to both sides: 52x ≤ 10

To isolate x, divide both sides by 52: x ≤ 10/52 = 5/26

Final answer: x ≤ 5/26

Hope this explanation helped!