Write an inequality to represent “7 less than the product of a number, n, and 16 is at most 45.” a. 7 – n + 16< 45 b. 16n ≤ 45 – 7 c. 16n – 7 ≤ 45

Option C.

Step-by-step explanation:

Let n ----> a number

we know that

The expression "the product of a number, n, and 16 " is equal to

The expression "7 less than the product of a number, n, and 16 " is equal to

The complete expression "7 less than the product of a number, n, and 16 is at most 45" is equal to

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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