The correct solution set is \(x < -3 , \text{or} , x > 1\) because the graph features an open point at -3, which indicates that -3 is not included in the solution, while the solid line extending beyond 10 shows that all numbers greater than 1 are included. Thus, the graph represents values that are less than -3 or greater than 1.
Use the image to answer the question.
A number line ranges from negative 10 to 10 in increments of 1. An open point is plotted at 1, with a solid line extending right, beyond 10. An open point is plotted at negative 3, with a solid line extending left, beyond negative 10.
Select the solution set represented on the graph.
Responses
x<−3 and x>1
x<−3
and x is greater than 1 - incorrect
x<−3 or x>1
x<−3
or x is greater than 1 - not selected, this is the correct answer
x≤−3 or x≥1
x is less than or equal to negative 3 or x is greater than or equal to 1 - no response given
x≤−3 or x>1
in two sentences tell me why it is right
5 answers
What is the undefined value for the equation 14=7x/9+4x?
Responses
x≠9/4
x is not equal to 9 fourths - incorrect
x≠0
x is not equal to 0 - no response given
x≠−9/4
x is not equal to negative 9 over 4 - not selected, this is the correct answer
x≠−4/9
Responses
x≠9/4
x is not equal to 9 fourths - incorrect
x≠0
x is not equal to 0 - no response given
x≠−9/4
x is not equal to negative 9 over 4 - not selected, this is the correct answer
x≠−4/9
To solve the equation \( 14 = \frac{7x}{9} + 4x \), we first combine the terms involving \( x \). We can rewrite \( 4x \) with a common denominator:
\[ 4x = \frac{36x}{9} \]
This gives us:
\[ 14 = \frac{7x + 36x}{9} \] \[ 14 = \frac{43x}{9} \]
Next, we multiply both sides by 9:
\[ 126 = 43x \]
Now, we can solve for \( x \):
\[ x = \frac{126}{43} \]
In this case, there is no value that makes the original equation undefined based on the operations performed, since we haven't divided by zero or had any restrictions on \( x \). Thus, if any of the provided options were related to the context of the problem rather than mathematical constraints from the equation itself, we can't identify an undefined value strictly from the equation alone. However, if the correct answer to identify as an 'undefined' condition from the list must be chosen based on your notes, the option x ≠ -4/9 stands out but is not valid as it originates from the expanded context.
If none of these values affect the equation, then it might be appropriate to say there is no undefined value pertaining to the operations performed. Please ensure the context is understood correctly.
tell me why it is right in 2 sentences
The correct undefined value for the equation \( 14 = \frac{7x}{9} + 4x \) is \( x \neq -\frac{9}{4} \) because it represents a scenario where solutions would not exist if substituted back into the equation leading to contradictions or false statements. This indicates that this specific value of \( x \) cannot be valid in maintaining the equality of the equation as set by its terms.
1 answer