88 less than the product 131313 times a number xxx is less than or equal to -32.−32.minus, 32, point write an inequality for the statement above. find the solution set of the inequality. write the solution using a fraction or integer.

The product 13 times x is written 13x. 8 less than that value can be written as

... 13x - 8

We want this to be indicated as being less than or equal to -32, so we write

... 13x - 8 ≤ -32

The operations performed on x are multiplication by 13 and subtraction of 8. To solve the inequality, we undo these operations in reverse order. To undo the subtraction, we add 8

... 13x ≤ -24

To undo the multiplication, we divide by the coefficient of x, which is 13. Dividing by 13 gives

... x ≤ -24/13 . . . . . this is the solution to the inequality

You can see that solving an inequality is very similar to solving an equation. The one difference is that the relationship symbol must be reversed when multiplying or dividing by a negative number. To see that this is true, you can consider a simple example:

... 2 > 1

Multiplying by -1 gives

... -2 < -1

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

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