Answer:To graph the expression 4(x - 6) - 10x + 15 on a number line, we need to simplify the expression and identify the solution.
Let's start by simplifying the expression:
4(x - 6) - 10x + 15
First, we apply the distributive property by multiplying 4 to both terms inside the parentheses:
4 * x = 4x
4 * -6 = -24
The expression becomes:
4x - 24 - 10x + 15
Next, we combine like terms:
(4x - 10x) + (-24 + 15)
-6x - 9
Now, we have the simplified expression -6x - 9. To graph it on a number line, we need to identify the x-values for which the expression equals zero.
Setting -6x - 9 equal to zero, we solve for x:
-6x - 9 = 0
Adding 9 to both sides:
-6x = 9
Dividing by -6:
x = -9/6
Simplifying:
x = -3/2 or -1.5
So, the expression equals zero when x is equal to -3/2 or -1.5.
To graph this on a number line, we mark these two points:
-3/2 and -1.5
Then, we draw a line between them to represent all the values of x where the expression equals zero.
On the number line, it would look like this:
-----------◄-3/2----◄-1.5-----------
Step-by-step explanation:
