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
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
To solve the inequality -36 < -5x - 6, we can first isolate the variable by adding 6 to both sides:
-36 + 6 < -5x
-30 < -5x
Next, divide both sides by -5. Remember to flip the inequality sign when dividing by negative number:
-30/-5 > x
6 > x
So the first part of the solution is x < 6.
Now let's solve the inequality -5x - 6 < -46 by adding 6 to both sides:
-5x - 6 + 6 < -46 + 6
-5x < -40
Divide both sides by -5, remembering to flip the inequality sign:
(-5x)/-5 > -40/-5
x > 8
So the second part of the solution is x > 8.
Combining the two solutions, we have x < 6 or x > 8.
On the number line, we place an open circle at 6 (since x is not equal to 6), and shade the region to the left of 6 to represent x < 6. Then, we place an open circle at 8 (since x is not equal to 8), and shade the region to the right of 8 to represent x > 8.