Apply the distributive property to create an equivalent equation.
3(2m + 7) = -5(6 + m)

6m + 42 = -30 - 5m

Step-by-step explanation:

distribute 3(2m+7) = -5(6+m)

6m + 42 = -30 - 5m

m=-51/11

Step-by-step explanation:

3(2m+7)=−5(6+m)

Simplify both sides of the equation.

3(2m+7)=−5(6+m)

(3)(2m)+(3)(7)=(−5)(6)+(−5)(m)

6m+21=−30+−5m

6m+21=−5m−30

Add 5m to both sides.

6m+21+5m=−5m−30+5m

11m+21=−30

Subtract 21 from both sides.

11m+21−21=−30−21

11m=−51

Divide both sides by 11.

Here's what I get.

Step-by-step explanation:

(a) x + 3y ≤ 8

(b) x +   y ≥ 2

Part A

(i) Inequality (a)

Solve for y

The graph of y ≥ ⅓(8-x) is represented by the upper red line and all points in the shaded area below it. The line is solid because points on the line satisfy the condition.

ii) Inequality (b)

Solve for y

The graph of y ≥ 2 - x is represented by the lower blue line and all points in the shaded area above it. The line is solid because points on the line satisfy the condition.

The solution set lies in the purple area. It consists of all combinations of x and y that make y ≥ ⅓(8 - x) and y ≥ 2 - x.

A practical but not a mathematical condition is that all values of x and y must be zero or positive numbers (for example, you can't have -2 servings of food), so I have plotted only the numbers in the first quadrant.

Part B

Substitute (8,2)into each inequality

(i) Inequality (a)

FALSE.

ii) Inequality (b)

TRUE.

The point (8, 2) satisfies one inequality but not the other.

It is in the blue area but not the purple area of the graph, so it is not in the solution area for the system.

Part C

I will choose the point (2, 1).

x + 3y = 2 + 3×1 =2 + 3 = 5

x + y = 3

x represents a serving of dry food and y represents a serving of wet food.

The point (2, 1) means that she can buy three servings of food (> 2) —  two of dry and one of wet) —  for $5 (< $8).