solve and graph

2x+9 greater or equal to 5 and 2x-13 greater or equal to -9

the solution is {x x greater or equal to ?}

What is the ? help

Please only post your questions once. Repeating posts will not get a quicker response. In addition, it wastes our time looking over reposts that have already been answered in another post. Thank you.

See my response to one of your previous posts.

To solve the inequality 2x + 9 ≥ 5, we can start by subtracting 9 from both sides of the inequality:

2x + 9 - 9 ≥ 5 - 9

Simplifying, we get:

2x ≥ -4

To isolate x, divide both sides of the inequality by 2:

2x/2 ≥ -4/2

x ≥ -2

So the solution to the first inequality is x ≥ -2.

Now, let's solve the second inequality, 2x - 13 ≥ -9. To isolate x, we can start by adding 13 to both sides:

2x - 13 + 13 ≥ -9 + 13

Simplifying, we get:

2x ≥ 4

Dividing both sides of the inequality by 2:

2x/2 ≥ 4/2

x ≥ 2

So the solution to the second inequality is x ≥ 2.

Now, to find the overall solution to both inequalities, we need to find the intersection of the solutions of each inequality. In other words, we need to find the values of x that satisfy both x ≥ -2 and x ≥ 2.

Since both inequalities require x to be greater than or equal to a certain value, the overall solution is the values of x that are greater than or equal to the larger value -2:

{x | x ≥ -2}

Graphically, this solution can be represented by a shaded region on the number line to the right of -2.