Solve for xx and graph the solution on the number line below. minus, 1, is greater than or equal to, minus, 11, plus, x −1≥ −11+x Answer Attempt 1 out of 3 is less than< is greater than> is less than or equal to≤ is greater than or equal to≥ or or Inequality Notation: 10≥x Number Line: 0 20 Click and drag to plot line. -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
To solve the inequality, we will start by isolating the variable x on one side of the inequality.
-1 ≥ -11 + x - 1
We can simplify the expression by combining like terms:
-1 ≥ -12 + x
Next, we will isolate x by subtracting x from both sides:
-1 - x ≥ -12 + x - x
This simplifies to:
-x - 1 ≥ -12
To solve for x, we will multiply both sides of the inequality by -1, remembering to reverse the inequality sign since we are multiplying by a negative number:
(-1)(-x - 1) ≤ (-1)(-12)
This simplifies to:
x + 1 ≤ 12
Finally, we will subtract 1 from both sides to isolate x:
x + 1 - 1 ≤ 12 - 1
This simplifies to:
x ≤ 11
So the solution to the inequality is x ≤ 11.
To graph the solution on the number line, we will plot a closed circle at 11 and draw an arrow to the left to show all values of x less than or equal to 11.
Number Line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
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