Solve the inequality. Graph and check your solutions.
5/7 + a > - 2/7
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.
To solve the inequality 5/7 + a > -2/7, we will conduct the following steps:
Step 1: Subtract 5/7 from both sides of the inequality.
a > -2/7 - 5/7
Simplifying the right side, we have:
a > -7/7
Step 2: Simplify the right side:
a > -1
So, the solution to the inequality is a > -1.
To graph this solution, we will represent it on the number line as a shaded portion to the right of -1.
________>------------------------------
-1
To check the solution, we can choose any number greater than -1 and substitute it into the original inequality.
Let's choose a = 0:
5/7 + 0 > -2/7
Simplifying the left side:
5/7 > -2/7
Since 5/7 is greater than -2/7, the inequality is true when a = 0. Therefore, the solution a > -1 is valid.
To solve the inequality, we'll start by isolating the variable "a".
First, subtract "5/7" from both sides of the inequality:
a > -2/7 - 5/7
Simplifying the right side:
a > -7/7
Now, calculate the right side:
a > -1
This means that "a" must be greater than -1.
To graph the solution on a number line, draw a line with a point labeled -1, and draw an arrow to the right to indicate that the solution includes all values greater than -1.
As for checking the solutions, you can select a number greater than -1, substitute it into the original inequality, and see if it holds true. Let's choose 0:
5/7 + 0 > -2/7
Simplifying the left side:
5/7 > -2/7
Since 5/7 is greater than -2/7, the inequality is true when a = 0.
Therefore, any value of "a" greater than -1 will satisfy the inequality.