Answer: x≤ -0.5
Step-by-step explanation: Graph the two lines or solve for x:
2x – 6 ≥ 6(x – 2) + 8
2x – 6 ≥ 6x – 12 + 8
2x – 6 ≥ 6x – 4
-4x ≥ 2
x ≤ -1/2 [Inequality is reversed when multiplying or dividing by a negative number]
The number line is anything less than or equal to - 1/2
Or one can plot each side of the inequality and note the interception point (x = -(1/2)).
Answer:
The number line is shown below.
Step-by-step explanation:
We need to represent number that is less than 3 on a number line.
Let x be numbers.
So, .
Now, we have a number which represents x<3. Here 3 is not included in the solution set, so there is an open circle on 3 and left side of 3 are in the solution set.
The number line is shown below.
Answer:
(12,-6)
Step-by-step explanation:
we have
----> inequality A
---> inequality B
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
<u><em>Verify each point</em></u>
Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B
case 1) (0,-1)
Inequality A
----> is true
Inequality B
----> is not true
therefore
The ordered pair is not a solution of the system
case 2) (0,3)
Inequality A
----> is true
Inequality B
----> is not true
therefore
The ordered pair is not a solution of the system
case 3) (-6,-6)
Inequality A
----> is true
Inequality B
----> is not true
therefore
The ordered pair is not a solution of the system
case 4) (12,-6)
Inequality A
----> is true
Inequality B
----> is true
therefore
The ordered pair is a solution of the system (makes true both inequalities)