I have two different questions.
what is the set built notation of -11x-24<27-10x
and
write the slope intercept equation for the line with slope -5/6 and y intercept (0,4)
-11x-24<27-10x
-11x + 10x < 27 + 24
-x < 51
x > -51
I will let you put into the notation you are familiar with
second one:
since you are given the slope and the y-intercept, the equation can be simply stated as
y = (-5/6)x + 4
-11x-24 < 27-10x
combine similar terms:
-11x + 10x < 27 + 24
*when transposing terms to other side of equation, the sign must become the opposite*
then,
-x < 51
multiply by -1 to get positive x:
x > -51
*note that when all terms are multiplied or divided by a NEGATIVE number, the inequality sign becomes the opposite*
thus x is all real number greater than -51 or (-51, +infinity)
for the second question,
slope-intercept form is:
y = mx + b
where b is the y-intercept (y-coordinate of the y-intercept) and m is the slope,, thus:
y = (-5/6)x + 4
hope this helps. :)
For the first question, to find the set builder notation of the inequality -11x - 24 < 27 - 10x, you need to solve it for x.
Here's how you can do that:
1. Start by moving all terms with x to one side of the inequality:
-11x + 10x < 27 + 24 - 10x
Simplifying, we get:
-x < 51 - 10x
2. Add 10x to both sides to eliminate the -10x term:
-x + 10x < 51
This simplifies to:
9x < 51
3. Divide both sides of the inequality by 9 to solve for x:
x < 51/9
Simplifying further, we get:
x < 17/3
Therefore, the set builder notation for the inequality -11x - 24 < 27 - 10x is:
{x | x < 17/3}
For the second question, you need to write the slope-intercept equation, y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope (m) is -5/6 and the y-intercept is (0,4), the equation can be written as:
y = (-5/6)x + 4
In this equation, -5/6 represents the slope since it is the coefficient of x, and 4 is the y-coordinate of the y-intercept.
So, the slope-intercept equation for the line with slope -5/6 and y-intercept (0,4) is:
y = (-5/6)x + 4