Solve the inequality. Graph the solution set and write it in interval notation.
negative 6 left parenthesis x minus 5 right parenthesis minus 4 x
less than
negative left parenthesis 5 x plus 6 right parenthesis plus 4 x
Question content area bottom
Part 1
Choose the correct graph below.
B.
An infinite number line has a tick mark labeled 0. The region to the right of a left parenthesis labeled 4 is shaded.
0
4
Your answer is correct.
Part 2
Write the answer in interval notation.
enter your response here
The solution set in interval notation is (-∞, 4).
no
I'm sorry, but there seems to be a misunderstanding. Can you please clarify which part of the question you are referring to?
To solve the inequality and graph the solution set, we need to simplify the expression first. Let's start by expanding the equation:
-6(x - 5) - 4x < -(5x + 6) + 4x
Simplifying each side:
-6x + 30 - 4x < -5x - 6 + 4x
Combining like terms:
-10x + 30 < -x - 6
Next, we want to isolate the variable, so let's move all the terms involving 'x' to one side and the constant terms to the other side:
-10x + x < -6 - 30
Simplifying further:
-9x < -36
To solve for 'x', we need to divide both sides of the inequality by -9. However, we have to keep in mind that dividing by a negative number will reverse the inequality sign:
x > -36 / -9
Simplifying the right-hand side:
x > 4
So, the solution to the inequality is x > 4.
To graph the solution set, we start with an infinite number line and label a tick mark at 0. Since the solution is x > 4, we shade the region to the right of the tick mark labeled 4.
The correct graph is B, where the region to the right of the tick mark labeled 4 is shaded.
As for interval notation, the solution x > 4 can be written as [4, ∞) which represents all values greater than or equal to 4, inclusively.
So, the answer in interval notation is [4, ∞).