Solve for xx and graph the solution on the number line below.
minus, 8, is greater than or equal to, minus, 8, x
−8≥
−8x
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
To solve this inequality, we can start by isolating x. We do this by dividing both sides of the inequality by -8, while remembering to reverse the direction of the inequality since we are dividing by a negative number:
-8 ≥ -8x
Dividing both sides by -8:
(-8)/(-8) ≤ (-8x)/(-8)
1 ≤ x
So the solution to the inequality is x ≥ 1.
On the number line, we can represent this as a closed circle at 1, and shading everything to the right of 1 to represent all the values of x that are greater than or equal to 1.
Number Line:
--------------●--------------
1
The filled-in circle represents 1, and the shading to the right of 1 represents all values of x greater than or equal to 1.
Solve for xx and graph the solution on the number line below.
36, is greater than, minus, 9, x
36>
−9x
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
To solve this inequality, we can start by isolating x. We do this by dividing both sides of the inequality by -9, but we also need to remember to reverse the direction of the inequality since we are dividing by a negative number:
36 > -9x
Dividing both sides by -9:
(36)/(-9) < (-9x)/(-9)
-4 < x
So the solution to the inequality is x > -4.
On the number line, we can represent this as an open circle at -4, and shading everything to the right of -4 to represent all the values of x that are greater than -4.
Number Line:
-----------○-----------
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
The open circle represents -4, and the shading to the right of -4 represents all values of x greater than -4.
Solve for xx and graph the solution on the number line below.
minus, 10, x, is greater than or equal to, 50
−10x≥
50
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
To solve this inequality, we can start by isolating x. We do this by dividing both sides of the inequality by -10, while remembering to reverse the direction of the inequality since we are dividing by a negative number:
−10x ≥ 50
Dividing both sides by -10:
(-10x)/(-10) ≥ (50)/(-10)
x ≤ -5
So the solution to the inequality is x ≤ -5.
On the number line, we can represent this as a closed circle at -5, and shading everything to the left of -5 to represent all the values of x that are less than or equal to -5.
Number Line:
--------------●--------------
-5
The filled-in circle represents -5, and the shading to the left of -5 represents all values of x less than or equal to -5.
Solve for xx and graph the solution on the number line below.
minus, 20, is greater than or equal to, 10, x
−20≥
10x
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
To solve this inequality, we can start by isolating x. We do this by dividing both sides of the inequality by 10:
-20 ≥ 10x
Dividing both sides by 10:
(-20)/10 ≥ (10x)/10
-2 ≥ x
So the solution to the inequality is x ≤ -2.
On the number line, we can represent this as a closed circle at -2, and shading everything to the left of -2 to represent all the values of x that are less than or equal to -2.
Number Line:
--------●---------------
-3 -2 -1 0 1 2 3 4 5
The filled-in circle represents -2, and the shading to the left of -2 represents all values of x less than or equal to -2.
Solve for xx and graph the solution on the number line below.
minus, 90, is greater than, minus, 9, x
−90>
−9x
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
To solve this inequality, we can start by isolating x. We do this by dividing both sides of the inequality by -9, but we also need to remember to reverse the direction of the inequality since we are dividing by a negative number:
-90 > -9x
Dividing both sides by -9:
(-90)/(-9) < (-9x)/(-9)
10 < x
So the solution to the inequality is x > 10.
On the number line, we can represent this as an open circle at 10, and shading everything to the right of 10 to represent all the values of x that are greater than 10.
Number Line:
-----------○-----------
9 10 11 12 13 14 15
The open circle represents 10, and the shading to the right of 10 represents all values of x greater than 10.