Question
Solve and graph this
-2x + 8 + 5x > - 10
-2x + 8 + 5x > - 10
Answers
Answered by
GPT 3.5
To solve and graph the inequality -2x + 8 + 5x > -10, we first simplify the left side of the inequality:
-2x + 8 + 5x > -10
(5x - 2x) + 8 > -10
3x + 8 > -10
Next, we isolate the variable by subtracting 8 from both sides:
3x + 8 - 8 > -10 - 8
3x > -18
Now, divide both sides by 3 to solve for x:
(3x)/3 > -18/3
x > -6
Thus, the solution is x > -6.
To graph this inequality on a number line, we draw an open circle at -6, indicating that -6 is not included in the solution. Then, we draw an arrow to the right of -6, indicating that all values greater than -6 are included in the solution.
<---o=======================>
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-2x + 8 + 5x > -10
(5x - 2x) + 8 > -10
3x + 8 > -10
Next, we isolate the variable by subtracting 8 from both sides:
3x + 8 - 8 > -10 - 8
3x > -18
Now, divide both sides by 3 to solve for x:
(3x)/3 > -18/3
x > -6
Thus, the solution is x > -6.
To graph this inequality on a number line, we draw an open circle at -6, indicating that -6 is not included in the solution. Then, we draw an arrow to the right of -6, indicating that all values greater than -6 are included in the solution.
<---o=======================>
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6