find the answer of the set for the inequality −2 ≤ 1 − (2 + 4x) < 3?
−2 ≤ 1 − (2 + 4x) < 3
-3 ≤ -(2+4x) < 2
3 >= 2+4x > -2
1 >= 4x > -4
1/4 > x > -1
See the graph at
http://www.wolframalpha.com/input/?i=plot+y%3D+1+%E2%88%92+%282+%2B+4x%29%2C+y+%3D+-2%2C+y%3D3
To find the solution of the inequality −2 ≤ 1 − (2 + 4x) < 3, we need to simplify and solve it step by step.
Step 1: Simplify the inequality.
Start by simplifying the expression inside the parentheses:
1 - (2 + 4x) = 1 - 2 - 4x = -1 - 4x
Now, we have:
-2 ≤ -1 - 4x < 3
Step 2: Isolate the variable.
We want to isolate the variable on one side of the inequality. Let's move the -1 to the other side by adding 1 to all parts of the inequality:
-2 + 1 ≤ -1 + 1 - 4x < 3 + 1
-1 ≤ -4x < 4
Step 3: Divide by the coefficient of x.
We need to solve for x, so we can divide all parts of the inequality by -4. However, since we are dividing by a negative number, the direction of the inequality symbols will change:
-1/(-4) ≥ -4x/(-4) < 4/(-4)
1/4 ≥ x > -1
Step 4: Final solution.
The solution to the inequality is 1/4 (or 0.25) greater than or equal to x, and x is strictly greater than -1. In interval notation, the solution can be written as (-1, 1/4].
Please note that if you require the solution in a different format or need further clarification, feel free to ask!