Can someone check this for me please...

4x + 8 >= (that is greater and equal to) 4 and 2x - 13 >= -5

the solution: {x|x>= 4}
on the graph the highlighted line goes to the left...is this correct?

To solve the system of inequalities: 4x + 8 ≥ 4 and 2x - 13 ≥ -5, you need to solve each inequality separately and find the intersection of the solution sets.

Let's solve the first inequality: 4x + 8 ≥ 4
To isolate the variable x, we can start by subtracting 8 from both sides: 4x + 8 - 8 ≥ 4 - 8, which simplifies to 4x ≥ -4.
Next, divide both sides of the inequality by 4 to solve for x: (4/4)x ≥ (-4/4), which further simplifies to x ≥ -1.

Now let's solve the second inequality: 2x - 13 ≥ -5
Begin by adding 13 to both sides of the inequality: 2x - 13 + 13 ≥ -5 + 13, resulting in 2x ≥ 8.
To solve for x, divide both sides of the inequality by 2: (2/2)x ≥ 8/2, which simplifies to x ≥ 4.

Now we have the solution sets for each inequality: x ≥ -1 and x ≥ 4. To find the intersection of these solution sets, we consider the common elements. Since both inequalities have the condition x ≥ 4 in common, the final solution is x ≥ 4.

On the graph, this solution is represented by a shaded area to the right of x = 4, indicating that any value of x greater than or equal to 4 would satisfy both inequalities. Therefore, the highlighted line going to the left would be incorrect; it should go to the right.