Solve the inequality. Graph the solution set and write it in interval notation.
x - 5 >= - 7
Write the answer in interval notation.
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To solve the inequality, we need to isolate the variable x.
Starting with:
x - 5 >= -7
First, we can add 5 to both sides of the inequality:
x - 5 + 5 >= -7 + 5
Which simplifies to:
x >= -2
The solution set, or graph, of this inequality is all real numbers greater than or equal to -2. This can be represented on a number line as a closed circle at -2, and an arrow extending to the right.
In interval notation, this can be written as:
[-2, +∞)
To solve the inequality x - 5 >= -7, we can first add 5 to both sides of the inequality to isolate x:
x - 5 + 5 >= -7 + 5
This simplifies to:
x >= -2
To graph the solution set, we can draw a number line and mark all the points that satisfy the inequality. In this case, since x is greater than or equal to -2, we would shade the number line to the right of -2:
●---●---●---●---●---●---●---●---●
-5 -4 -3 -2 -1 0 1 2 3
Next, to write the answer in interval notation, we use brackets [ ] to show that -2 is included in the solution set. Since the values start at -2 and extend to positive infinity, the interval notation is:
[-2, ∞)
To solve this inequality, you want to isolate the variable x.
Step 1: Add 5 to both sides of the inequality:
x - 5 + 5 >= -7 + 5
x >= -2
This means that any value of x that is greater than or equal to -2 will satisfy the inequality.
To graph the solution set, you can represent it on the number line.
Start by drawing a number line and marking a point at -2. Then, shade the line to the right of -2 to indicate that any value greater than -2 is included in the solution set.
The graph would look like:
<img src="https://i.imgur.com/Rffkouh.png" height="200">
In interval notation, the solution set can be written as [-2, +∞). This notation represents all real numbers greater than or equal to -2, including -2 itself. The open square bracket indicates that -2 is included in the solution set, and the infinity symbol represents all possible values greater than -2.