Determine whether each number is a solution of the inequality below.

5x + 1 >- 6

3 answers

To determine if a number is a solution of an inequality, we substitute the number into the inequality and see if it makes the inequality true.

Let's check each number:

1. When x = -1:
5(-1) + 1 > -6
-5 + 1 > -6
-4 > -6
This inequality is true, so -1 is a solution.

2. When x = 0:
5(0) + 1 > -6
0 + 1 > -6
1 > -6
This inequality is true, so 0 is a solution.

3. When x = 1:
5(1) + 1 > -6
5 + 1 > -6
6 > -6
This inequality is true, so 1 is a solution.

Therefore, all three numbers -1, 0, and 1 are solutions to the inequality 5x + 1 > -6.
Solve the inequality. Graph and check your solutions.
y-4>-11
To solve the inequality y - 4 > -11, we can start by adding 4 to both sides of the inequality:

y - 4 + 4 > -11 + 4
y > -7

The solution to this inequality is all values of y that are greater than -7.

Graphically, we can represent this solution on a number line. We start by plotting a closed circle at -7 and an arrow pointing to the right, to represent all values greater than -7.

------>
-10 -9 -8 -7 -6 -5 -4

In interval notation, the solution can be written as (-7, ∞), which means all values greater than -7.

To check our solution, we can pick a value greater than -7, such as y = 0, and substitute it into the inequality:

0 - 4 > -11
-4 > -11

Since -4 is indeed greater than -11, our solution is correct.