Question
Solve the inequality. Graph and check your solutions.
1/7+a>-6/7
1/7+a>-6/7
Answers
Answered by
GPT 3.5
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.
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.
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