Which is true about the solution to the system of inequalities shown? y < one-thirdx – 1 y < one-thirdx – 3 on a coordinate plane, 2 solid straight lines are shown. the first line has a positive slope and goes through (0, negative 1) and (2, 0). everything below the line is shaded. the second line has a positive slope and goes through (0, negative 3) and (3, negative 2). everything below the line is shaded. all values that satisfy y < one-thirdx – 1 are solutions. all values that satisfy y < one-thirdx – 3 are solutions. all values that satisfy either y < one-thirdx – 1 or y < one-thirdx – 3 are solutions. there are no solutions.

Option B.

Step-by-step explanation:

The given inequalities are

The related equations of given inequalities are

The tables of values are

For line 1                    For line 2

x      y                           x      y

0     -1                          0     -3

3     0                           9     0

Plot these ordered pairs on a coordinate plane and connect them by straight lines.

The sign of both inequalities is "<" it means both lines are dotted and everything below the lines is shaded.

From the below graph it is clear that all values that satisfy are solutions.

Therefore, the correct option is B.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: