Question
Solve the inequality. Graph and check your solutions.
5/7 + a > - 2/7
5/7 + a > - 2/7
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Answered by
GPT 3.5
To solve the inequality, we need to isolate the variable "a" by moving the constant to the other side of the inequality sign.
5/7 + a > -2/7
Subtract 5/7 from both sides:
a > -2/7 - 5/7
a > -7/7
Simplifying the right side of the equation:
a > -1
Since the inequality symbol is greater than (>) and not greater than or equal to (≥), we use an open circle on -1 in the number line graph.
Checking the solution by substituting some values:
Let's try a value less than -1, such as a = -2:
5/7 + (-2) = 5/7 - 14/7 = -9/7
-9/7 is indeed greater than -2/7, so the solution is valid.
Let's try a value greater than -1, such as a = 0:
5/7 + 0 = 5/7
5/7 is also greater than -2/7, so the solution is valid.
Therefore, the solution to the inequality 5/7 + a > -2/7 is a > -1. This can be represented on a number line graph with an open circle at -1 and a shaded region to the right.
5/7 + a > -2/7
Subtract 5/7 from both sides:
a > -2/7 - 5/7
a > -7/7
Simplifying the right side of the equation:
a > -1
Since the inequality symbol is greater than (>) and not greater than or equal to (≥), we use an open circle on -1 in the number line graph.
Checking the solution by substituting some values:
Let's try a value less than -1, such as a = -2:
5/7 + (-2) = 5/7 - 14/7 = -9/7
-9/7 is indeed greater than -2/7, so the solution is valid.
Let's try a value greater than -1, such as a = 0:
5/7 + 0 = 5/7
5/7 is also greater than -2/7, so the solution is valid.
Therefore, the solution to the inequality 5/7 + a > -2/7 is a > -1. This can be represented on a number line graph with an open circle at -1 and a shaded region to the right.
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