Consider the equation 12=6x8x−5

Question

Which term helps determine the equation's undefined value?

(1 point)
Responses

12
12

8x−5
8 x minus 5

6x
6 x
Question 2
Find the undefined value.(1 point)
x≠

Answer 1

To determine the undefined value of the equation \( 12 = 6x \cdot (8x - 5) \), we need to identify the term that can cause the equation to be undefined.

The term that helps determine the undefined value is \( 8x - 5 \). This term could be equal to zero, which would result in an undefined situation in the context of the equation.

To find the undefined value, we set \( 8x - 5 = 0 \):

\[ 8x - 5 = 0 \] \[ 8x = 5 \] \[ x = \frac{5}{8} \]

Thus, the undefined value is:

\[ x \neq \frac{5}{8} \]

Responses:

1. The term that helps determine the equation's undefined value: 8x - 5
2. The undefined value: x ≠ \(\frac{5}{8}\)

Answer 2

Solve for s
in the following equation: 12s+5+7=8
(2 points)
s =

Answer 3

To solve for \( s \) in the equation \( 12s + 5 + 7 = 8 \), follow these steps:

1. Combine like terms on the left side of the equation: \[ 12s + (5 + 7) = 8 \implies 12s + 12 = 8 \]

2. Subtract 12 from both sides: \[ 12s + 12 - 12 = 8 - 12 \implies 12s = -4 \]

3. Divide both sides by 12: \[ s = \frac{-4}{12} \implies s = \frac{-1}{3} \]

The solution is: \[ s = -\frac{1}{3} \]

Answer 4

Given the formula for time (t
) in terms of distance (d
) and velocity (v
), t=dv
, what operation would you use to isolate the distance?(2 points)
Responses

addition
addition

subtraction
subtraction

multiplication
multiplication

division

Answer 5

The formula for time \( t \) in terms of distance \( d \) and velocity \( v \) is given by:

\[ t = \frac{d}{v} \]

To isolate distance \( d \), you need to eliminate the velocity \( v \) from the right side of the equation. Since \( d \) is divided by \( v \), you would perform the inverse operation of division, which is multiplication.

Thus, you would multiply both sides of the equation by \( v \):

\[ d = t \cdot v \]

Response:

Multiplication

Answer 6

Sebastian needed to buy new tires for his car. The tire shop was running a holiday deal that allowed customers to buy three tires and get the fourth tire for $10. If the total price for all his tires was $254.50, what was the cost of each of the first three tires?(2 points)
$

Answer 7

Let's denote the cost of each of the first three tires as \( x \). According to the deal, if he buys three tires, the fourth tire costs $10. Therefore, the total cost can be expressed by the equation:

\[ 3x + 10 = 254.50 \]

Now, we can solve for \( x \):

1. Subtract $10 from both sides to isolate the cost of the three tires: \[ 3x = 254.50 - 10 \] \[ 3x = 244.50 \]

2. Next, divide both sides by 3 to find the cost of one tire: \[ x = \frac{244.50}{3} \] \[ x = 81.50 \]

Thus, the cost of each of the first three tires is:

\[ \boxed{81.50} \]

Answer 8

Using the properties of inequality, justify both steps in solving the inequality 25m−8<−2
.(2 points)
25m−8<−2

25m−8+8<−2+8


52(25m)<52(6)


Question 2
Solve for m
(1 point)

Answer 9

Let's solve the inequality step by step and justify each operation.

1. Starting Inequality: \[ 25m - 8 < -2 \]

2. Step 1: Add 8 to both sides: \[ 25m - 8 + 8 < -2 + 8 \] The justification for this step is the addition property of inequalities, which states that if \( a < b \), then \( a + c < b + c \) for any real number \( c \). Here, \( c = 8 \).

   After performing the operation: \[ 25m < 6 \]

3. Step 2: Divide both sides by 25: \[ \frac{25m}{25} < \frac{6}{25} \] The justification for this step is the division property of inequalities, which states that if \( a < b \) and \( c > 0 \), then \( \frac{a}{c} < \frac{b}{c} \). Here, \( c = 25 \), which is greater than 0.

   So, after this operation: \[ m < \frac{6}{25} \]

Question 2 - Solve for \( m \):

Thus, the solution to the inequality is:

\[ \boxed{m < \frac{6}{25}} \]

Answer 10

Consider the equation 5x3x−15+7=14
(1 point)
Which part of the fraction determines if it is undefined?

Question 2
(2 points)
Therefore, for the equation to be defined,
≠0

This means that x≠

Answer 11

To analyze the equation given:

\[ 5x \cdot (3x - 15) + 7 = 14 \]

Let's simplify it for clarity. The fraction isn't directly evident in your equation. However, if you are referring to potential division by a term that could be zero, we can proceed with that assumption. If the equation was implied to have any fraction, it can often stem from rearranging the equation.

Question 1

1. Which part of the fraction determines if it is undefined?

If there was a term like \( 3x - 15 \) acting as a denominator in a fraction, that could lead to being undefined if equal to zero.

2. Identifying the term:
   • The term sometimes leading to an undefined value would be \( 3x - 15 \).

Question 2

To determine under what conditions this term does not equal zero:

• Set the term to zero: \[ 3x - 15 = 0 \]
• Solving for \( x \): \[ 3x = 15 \ x = 5 \]

Therefore, for the equation to be defined: \[ 3x - 15 \neq 0 \] This means that: \[ x \neq 5 \]

Final Answers:

1. The term that determines if the equation is undefined: \( 3x - 15 \)
2. Therefore, for the equation to be defined: \( x \neq 5 \)