Solve the inequality. Graph and check your solutions.
1/2+a>-3/2
To solve the inequality 1/2 + a > -3/2, we can subtract 1/2 from both sides:
a > -3/2 - 1/2
Simplifying the right side:
a > -4/2
a > -2
To graph the solution, we can plot an open circle at -2 on the number line since the inequality is "greater than" and not "greater than or equal to".
To check the solutions, we can pick a value greater than -2, such as 0, and substitute it into the original inequality:
1/2 + 0 > -3/2
1/2 > -3/2
Since 1/2 is greater than -3/2, the inequality holds true for this value.
Therefore, the solution is a > -2, and it can be graphed as an open circle at -2 on the number line.
To solve the inequality 1/2 + a > -3/2, you can follow these steps:
Step 1: Subtract 1/2 from both sides of the inequality to isolate the variable a:
1/2 + a - 1/2 > -3/2 - 1/2
a > -4/2
Simplifying further:
a > -2
Step 2: Graph the solution on a number line.
We need to graph all values of a that are greater than -2 (excluding -2 itself). To do this, draw an open circle at -2 and shade all values to the right of it on the number line.
-2----o------------------------>
Step 3: Check the solution.
To check the solution, substitute a value greater than -2 (e.g., a = 0) into the original inequality and see if it holds true.
1/2 + a > -3/2
1/2 + 0 > -3/2
1/2 > -3/2
The inequality is true, so the solution is valid.
Therefore, the graph of the inequality 1/2 + a > -3/2 is an open circle at -2 with all values greater than -2 shaded to the right.
To solve the inequality 1/2 + a > -3/2, we can follow these steps:
Step 1: Subtract 1/2 from both sides of the inequality:
1/2 + a - 1/2 > -3/2 - 1/2
a > -4/2
Step 2: Simplify the right side:
a > -2
So, the solution to the inequality is a > -2.
To graph the solution on a number line, we draw an open circle above -2 (since it's not inclusive) and shade the region to the right of -2, indicating that any value greater than -2 is a solution.
Checking the solution:
Let's choose a value p that is greater than -2 and substitute it into the inequality.
For example, let p = 0. If we plug it into the inequality, we get:
1/2 + 0 > -3/2
1/2 > -3/2
This is true, so p = 0 is a valid solution to the inequality.
Similarly, if we choose a value that is less than -2, such as q = -3, and substitute it into the inequality:
1/2 + (-3) > -3/2
1/2 - 3 > -3/2
-5/2 > -3/2
This is also true, so q = -3 is a valid solution to the inequality.
By checking more values, we would find that any value greater than -2 satisfies the inequality.