Solve the inequality. Graph and check your solution.
x/2 >= - 4;
x >= - 8 (Simplify your answer.)
Choose the correct graph below.
The correct graph represents all the values of x greater than or equal to -8. It should be a number line with a closed circle at -8 and an arrow to the right indicating all the values of x that satisfy the inequality x >= -8.
To solve the inequality x/2 >= -4, we need to multiply both sides of the inequality by 2 to eliminate the fraction.
x/2 * 2 >= -4 * 2
x >= -8
So the solution to the inequality is x >= -8.
To graph the solution, we draw a number line and put a closed circle at -8 because it is included in the solution. Since x is greater than or equal to -8, we shade to the right of -8 on the number line.
The correct graph would be a closed circle at -8 with a shaded line extending to the right.
To solve the inequality, x/2 >= -4, we need to follow these steps:
Step 1: Multiply both sides of the inequality by 2 to eliminate the fraction:
2 * (x/2) >= 2 * (-4)
x >= -8
Step 2: Simplify the inequality, x >= -8.
Now, let's graph the solution x >= -8 on a number line. We represent the boundary point with a solid dot at -8, and draw an arrow to the right to indicate all values greater than -8 are solutions.
-8--------------------->
To check our solution, we can pick any value greater than -8, such as x = -7. Plugging x = -7 into the inequality, we get (-7)/2 >= -4, which simplifies to -7/2 >= -4. Since -7/2 is greater than -4, our solution is correct.
The correct graph for the solution x >= -8 is the number line with a solid dot at -8 and an arrow pointing towards positive infinity.