To solve the inequality, we can follow these steps:
-3x + 5 ≤ 23
First, we subtract 5 from both sides to isolate the variable:
-3x ≤ 23 - 5
-3x ≤ 18
Next, we divide both sides by -3. However, remember that when you divide by a negative number, the inequality changes direction:
x ≥ 18 / -3
x ≥ -6
The solution for this inequality is x ≥ -6.
To graph the solution on a number line, we start by plotting a closed circle on -6 since x is greater than or equal to -6. Then, we draw a line extending to the right to indicate all the numbers greater than -6.
------------------> (+∞)
-6 -5 -4 -3 -2 -1 0
So, the graph for the solution x ≥ -6 would look like this:
---------------------•---> (+∞)
-6 -5 -4 -3 -2 -1 0
solve and graph the solution for this inequality. -3x + 5 < 23 but the < has a line underneath it.
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