Solve the inequality. Graph and check your solutions.

Question

5/7 + a > - 2/7

Answer 1

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.