Question

1. this graph shows some solutions to ( 3x + 2ygeq12 ).

write an ordered pair for another point that is a solution to this inequality.

1. write an ordered pair for a point that is not a solution to ( 3x + 2ygeq12 ).

spiral review
problems 8 - 9: write an inequality for each situation.

1. duri will stay warm in a sleeping bag when the temperature is at least ( 30^{circ}f ).

use ( t ) to represent temperatures at which duri will stay warm.

1. duris backpack needs to weigh less than 45 pounds. use ( w ) to represent the weight of the backpack.

problems 10 - 11: here is an equation: ( 6x + 2y = 36 ).

1. for each value of ( x ), determine the value of ( y ).
2. which equation represents the same relationship?

a. ( y = 6 - 3x ) b. ( y = 18 - 3x ) c. ( y = 18-\frac{1}{3}x ) d. ( y = 6-\frac{1}{3}x )
reflection

1. circle the problem you enjoyed doing the most.
2. use the space to ask a question or share something youre proud of

Explanation:

Problem 6

Step1: Choose a value for \(x\)

Let \(x = 5\).

Step2: Substitute into the inequality and solve for \(y\)

Substitute \(x = 5\) into \(3x+2y\geq12\):
\(3\times5 + 2y\geq12\)
\(15+2y\geq12\)
\(2y\geq12 - 15\)
\(2y\geq - 3\)
\(y\geq-\frac{3}{2}\)
We can choose \(y = 0\) (since \(0\geq-\frac{3}{2}\))

Step1: Choose a value for \(x\)

Let \(x = 0\)

Step2: Substitute into the inequality and solve for \(y\)

Substitute \(x = 0\) into \(3x + 2y\geq12\):
\(3\times0+2y\geq12\)
\(2y\geq12\)
\(y\geq6\)
If we choose \(y = 0\) (since \(0<6\))

The phrase "at least" means greater than or equal to.

Answer:

\((5,0)\) (other valid answers are possible)

Problem 7