Solve for xx and graph the solution on the number line below.
minus, 36, is less than, minus, 5, x, minus, 6, or, minus, 5, x, minus, 6, is less than, minus, 46
−36<−5x−6or
−5x−6<−46
To solve the inequality -36 < -5x - 6, we can first add 6 to both sides to isolate the term with x:
-36 + 6 < -5x
-30 < -5x
Next, we divide both sides by -5, remembering to reverse the inequality sign since we are dividing by a negative number:
-30/-5 > x
6 > x
So the first part of the solution is x < 6.
Next, let's solve the inequality -5x - 6 < -46 by adding 6 to both sides:
-5x - 6 + 6 < -46 + 6
-5x < -40
Then, divide both sides by -5, remembering to reverse the inequality sign:
-5x/-5 > -40/-5
x > 8
So the second part of the solution is x > 8.
Combining the two parts, we have x < 6 or x > 8.
Graphing this solution on a number line:
---------------------o---------o---------------------
6 8
The solution is all values of x that are to the left of 6 or to the right of 8, including both of the endpoints.