Fifteen subtracted from the product of a number and -4 is at most 32

Step-by-step explanation:

Let's use the variable x to represent the unknown number.  

Also, the word, "product", indicates multiplication.  

In this problem, the product of a number and -4 would be represented as -4 x

The words, "is at most", would be represented as:  <

Then to create the inequality, subtract 15:

-4 x - 15 <  32

Now solve the inequality using inverse operations.  NOTE - Be sure to reverse the direction of the inequality symbol when multiplying or dividing by a negative number.

4 x - 15 < 32

-4 x - 15  + 15 < 32 + 15

-4 x < 47

-4 x / -4 >  47/-4

x  >  -47/4    

x  >  -11.75

Hope this helped!

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true