Graph the solution set for the inequality: −3x+1≤−47
(1 point)
Responses
To graph the solution set for the inequality −3x+1≤−47, we first need to isolate the variable x.
Let's start by subtracting 1 from both sides of the inequality:
−3x + 1 - 1 ≤ -47 - 1
−3x ≤ -48
Next, divide both sides of the inequality by -3. Remember that when dividing by a negative number, we need to reverse the inequality sign:
−3x/(-3) ≥ -48/(-3)
x ≥ 16
So the solution set for the inequality is x ≥ 16.
To graph this inequality, we draw a number line and mark a closed circle at 16, since x can be equal to 16. Then, we shade the region to the right of 16 to indicate that x is greater than or equal to 16.
Here is a graph of the solution set:
-47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
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∞
To graph the solution set for the inequality −3x + 1 ≤ −47, you can start by rewriting the inequality in slope-intercept form (y = mx + b) where y is replaced with −3x + 1:
−3x + 1 ≤ −47
Subtracting 1 from both sides:
−3x ≤ −48
Dividing both sides by −3 (remember to flip the inequality when dividing by a negative number):
x ≥ 16
This means that any value of x that is greater than or equal to 16 is a solution to the inequality.
To graph the solution set on a number line, you can start by drawing a line and marking a point at 16. Then, shade all the values to the right of 16 (including 16) to represent the set of numbers that are greater than or equal to 16.
The graph will look like this:
<-------------------|------------->
-1 16
The shaded part of the line represents the solution set for the inequality −3x + 1 ≤ −47.