Solve the inequality. Graph and check your solutions.
5/7 + a > - 2/7
Choose the correct graph below.
To solve the inequality 5/7 + a > -2/7, we need to isolate the variable a.
Subtract 5/7 from both sides of the inequality:
a > -2/7 - 5/7
a > -7/7
Simplify:
a > -1
To graph the solution, we use an open circle on -1 to indicate that it is not included in the solution. Then, we shade to the right of -1 to represent all values greater than -1.
The correct graph is the one with an open circle on -1 and shading to the right.
Sorry, I cannot generate a graph. However, I can solve and check the inequality for you.
To solve the inequality 5/7 + a > -2/7, we can start by subtracting 5/7 from both sides:
5/7 + a - 5/7 > -2/7 - 5/7
a > -7/7 - 5/7
Simplifying further:
a > -12/7
So we can represent the solution graphically as all the numbers greater than -12/7 on the number line. We can mark -12/7 with an open circle since it is not included in the solution. Any value greater than -12/7 will be included in the solution.
To solve the inequality 5/7 + a > -2/7, we can follow these steps:
Step 1: Subtract 5/7 from both sides of the inequality:
(5/7 + a) - 5/7 > (-2/7) - 5/7
a > -7/7
Step 2: Simplify the expression on the right side:
a > -1
Now, let's graph and check the solutions.
To graph the solution, we draw a number line and plot the point -1 by making an open circle at -1 and shading the line to the right. The open circle indicates that -1 is not included in the solution set.
---------------------o------------------------>
...-3 -2 -1 0 1 2 3 ...
The arrow on the right indicates that the shaded region extends infinitely in that direction.
Next, we need to check the solutions. We can pick any number greater than -1 and substitute it back into the inequality to see if it holds true. For example, let's use 0:
5/7 + a > -2/7
5/7 + 0 > -2/7
5/7 > -2/7
Since 5/7 is greater than -2/7, the inequality is true. We can do this check with any number greater than -1 to confirm that the solution set lies to the right of -1 on the number line.