2x+15 >= 13 and 2x-13 >= -5?
solve and graph
2x+15 >= 13
2x-13 >= -5
what's the solution x >= ?
and how does this appear on a line graph/number line?
2x>/=-2
x >/= -1
2x>/= 8
x >/= 4
x = 4 and everything to the right of x = 4
2X + 15 >= 13.
2X - 13 >= -5
Add the 2 Eq.
4X + 2 >= 8
Solve for X
4X >= 6
X >= 3 / 2 >= 1 1/2.
Graph the solution:
1. Draw a filled -in circle(dot) on the number line at 1 1/2. This means that X = 1 1/2 is a part of the solution.
2. Starting at the dot, draw a straight line to the right on the number line. Extend this line pass all
numbers on the right of the dot,
which means all real numbers greater
than 1 1/2 are a part of the solution.
If your inequality did not have an
equal sign (x > 1 1/2), the procedure
would have been exactly the same
except the circle would be left open
(o) meaning the 1 1/2 is not a part of
the solution. But all numbers above
1 1/2 is a part of the solution.
I hope this is helpful.
To solve the inequalities and find the values of x that satisfy both conditions, we'll solve each inequality separately and then find their intersection.
Let's start with the first inequality: 2x + 15 ≥ 13
Subtracting 15 from both sides: 2x ≥ 13 - 15
Simplifying: 2x ≥ -2
Dividing both sides by 2 (remember we must reverse the inequality sign when dividing by a negative number): x ≥ -1
Now let's move to the second inequality: 2x - 13 ≥ -5
Adding 13 to both sides: 2x ≥ -5 + 13
Simplifying: 2x ≥ 8
Dividing both sides by 2: x ≥ 4
To find the values of x that satisfy both inequalities, we take their intersection, which is the values that satisfy both conditions: x ≥ 4.
On a number line or line graph, we represent this solution as a shaded region to the right of 4, including 4. We can draw an arrow or shade the line to the right of the number 4 to indicate that any value on or to the right of 4 is a valid solution. Values less than 4 are not included in the solution.