Question

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. Write and solve an inequality for the statement above. No need to graph.

Answer 1

To solve the inequality, we simplify the expression on both sides, combine like terms, and isolate the variable x. x ≤ 5/26

Step-by-step explanation:

To write and solve the inequality, we need to break down the given statement:

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.

The product of 6 and the difference of 6x and 3 is 6(6x - 3) = 36x - 18.

The product of -2 and the sum of 4 and 8x is -2(4 + 8x) = -8 - 16x.

So the inequality becomes:

36x - 18 ≤ -8 - 16x.

Now solve for x:

36x + 16x ≤ -8 + 18

52x ≤ 10

x ≤ 10/52

x ≤ 5/26