Solve the inequality. Graph and check your solutions.
1/7+a>-6/7
To solve the inequality 1/7 + a > -6/7, we need to isolate the variable "a". Let's start by subtracting 1/7 from both sides:
1/7 + a - 1/7 > -6/7 - 1/7
a > -7/7
Simplifying further, we have:
a > -1
The solution to the inequality is all values of "a" that are greater than -1. To graph this solution, we will use a number line. We will not include -1 in our solution because the inequality is strict (">"), not inclusive (">=").
On the number line, we can mark -1 with an open circle to indicate that it is not included. Then, we shade the region to the right of -1 to represent all values greater than -1:
<=====================(o)------------------->
-4 -3 -2 -1 0
Now let's check the solution. We can pick any value greater than -1 and substitute it into the original inequality to see if it holds true. Let's choose 0:
1/7 + (0) > -6/7
1/7 > -6/7
This inequality is true since 1/7 is greater than -6/7.
Therefore, the solution to the inequality is a > -1 and we can represent it graphically as a number line with an open circle on -1 and shading to the right.
To solve the inequality 1/7 + a > -6/7, we will follow these steps:
Step 1: Subtract 1/7 from both sides of the inequality:
1/7 + a - 1/7 > -6/7 - 1/7
a > -7/7 - 1/7
a > -8/7
Step 2: Simplify the right side of the inequality:
a > -8/7
Step 3: Graph the solution on a number line:
Since we have "a >" (greater than), we will use an open circle to represent the endpoint -8/7 and shade the region to the right of the endpoint.
```
-8/7 ∞
───────┬────────┬───────>
```
Step 4: Check the solution:
Choose a value greater than -8/7, let's say a = 0.
1/7 + 0 > -6/7
1/7 > -6/7 (True)
The inequality is satisfied for a = 0.
Therefore, the solution to the inequality is a > -8/7.
To solve the inequality 1/7 + a > -6/7, we need to isolate the variable a. Let's break down the steps:
Step 1: Subtract 1/7 from both sides of the inequality:
1/7 + a - 1/7 > -6/7 - 1/7
a > -7/7 - 1/7
a > -8/7
Step 2: Simplify the right side of the inequality:
a > -8/7
Now that we have solved the inequality, we can graph the solution on the number line and check the solutions.
To graph the solution, we'll make an open circle at -8/7 and draw an arrow to the right to represent all values of a greater than -8/7. This indicates that the solution includes all real numbers greater than -8/7.
On the number line, -8/7 would be placed between -2 and -1. We can label the point -8/7.
Now, let's check the solution by substituting a value greater than -8/7 into the original inequality and see if it holds true.
Let's choose a = 0. We substitute this value into the inequality:
1/7 + 0 > -6/7
1/7 > -6/7
Since 1/7 is indeed greater than -6/7, our solution holds true. We can also check with other values of a greater than -8/7, and we will find that the inequality remains true.
Therefore, the solution to the inequality 1/7 + a > -6/7 is a > -8/7, and it can be graphed with an open circle at -8/7 on the number line, and an arrow pointing to the right.