What is the solution of 2-(x+4)is greater than or equal to 3-2x by using interval notation
2 - (x + 4) >= 3 - 2x
2 - x - 4 >= 3 - 2x
-x - 2 >= -2x + 3
add x to each side
-2 >= -x + 3
subtract 3 from both sides
-5 >= -x
multiply through by -1, remembering to reverse the direction of the inequality
5 <= x
means
x >= 5
for interval notation use the square bracket when = is involved and the round bracket when it is not.
To find the solution of the inequality 2 - (x + 4) ≥ 3 - 2x, we can solve it step-by-step:
Step 1: Simplify both sides of the inequality:
2 - (x + 4) ≥ 3 - 2x.
2 - x - 4 ≥ 3 - 2x.
- x - 2 ≥ 3 - 2x.
Step 2: Move x terms to one side and the constant terms to the other side:
- x + 2x ≥ 3 + 2.
x ≥ 5.
Step 3: Write the solution in interval notation:
Since there are no restrictions on x, the solution is all real numbers greater than or equal to 5. In interval notation, this can be represented as [5, ∞).
To solve the inequality 2 - (x + 4) ≥ 3 - 2x, we can follow these steps:
Step 1: Distribute the negative sign:
2 - x - 4 ≥ 3 - 2x
Step 2: Combine like terms:
- x - 2 ≥ -2x + 3
Step 3: Move all the terms involving x to one side of the inequality:
- x + 2x ≥ 3 + 2
Step 4: Combine like terms again:
x ≥ 5
Now, to express the solution in interval notation, remember that x ≥ 5 means that x is greater than or equal to 5.
In interval notation, we use square brackets [ ] for inclusive endpoints (when the solution includes the value), and parentheses ( ) for exclusive endpoints (when the solution does not include the value).
Since the solution x = 5 is included, we use a square bracket for 5. Since there is no upper bound or exclusive endpoint, we use an infinity symbol (∞).
Thus, the solution in interval notation is [5, ∞).