Graph the inequality on the number line and then write it in interval notation.
8x+5(x+5)≥2x+58
Please can you help me with the interval notation and graph number line description ( where plot the point what direction the line arrow goes.)
8 x + 5 ( x + 5 ) ≥ 2 x + 58
8 x + 5 ∙ x + 5 ∙ 5 ≥ 2 x + 58
8 x + 5 x + 25 ≥ 2 x + 58
13 x + 25 ≥ 2 x + 58
13 x - 2 x ≥ 58 - 25
11 x ≥ 33
11 x / 11 ≥ 33 / 11
x ≥ 3
x ∈ ( 3 , ∞ )
If you want go on:
wolframalha.c o m
When page be open type:
8 x + 5 ( x + 5 ) ≥ 2 x + 58
and click option
=
You will see graph
wolframalpha.c o m
Thank You Bosnian because I am horrible in Math expectantly the graphing.
To begin, let's simplify the inequality:
8x + 5(x + 5) ≥ 2x + 58
Distribute to clear the parentheses:
8x + 5x + 25 ≥ 2x + 58
Combine like terms:
13x + 25 ≥ 2x + 58
Next, isolate the variable x by subtracting 2x from both sides:
13x - 2x + 25 ≥ 58
Simplifying:
11x + 25 ≥ 58
Now, subtract 25 from both sides:
11x + 25 - 25 ≥ 58 - 25
Simplifying:
11x ≥ 33
To finish solving for x, divide both sides of the inequality by 11:
11x/11 ≥ 33/11
Simplifying:
x ≥ 3
Now, let's graph the inequality on a number line:
First, draw a horizontal number line. Choose a point to represent 3 and plot it on the number line. Since the inequality is inclusive of 3 (x ≥ 3), plot a filled-in circle on the point.
Next, determine the direction of the inequality. The inequality x ≥ 3 means that x must be greater than or equal to 3. To indicate this on the number line, draw an arrow extending to the right from the filled-in circle.
Finally, write the inequality in interval notation:
The inequality x ≥ 3 can be expressed in interval notation as [3, ∞), where the square bracket indicates that 3 is included and the infinity symbol (∞) represents all values greater than 3.