Manipulate the equation y=5x-11 so that it is written in terms of x. Which equation is equivalent to y=5x-11?

Question

A.
x=(y/11) -5
B.
x= y+11/5

C. y-11/5

D.
x=(y/5) +11

Answer 1

To manipulate the equation \( y = 5x - 11 \) in terms of \( x \), follow these steps:

1. Start with the original equation: \[ y = 5x - 11 \]

2. Add 11 to both sides: \[ y + 11 = 5x \]

3. Divide both sides by 5 to isolate \( x \): \[ x = \frac{y + 11}{5} \]

Now, let's check which of the options matches this equation:

A. \( x = \frac{y}{11} - 5 \) → not equivalent.

B. \( x = \frac{y + 11}{5} \) → this matches what we derived.

C. \( y - \frac{11}{5} \) → not equivalent.

D. \( x = \frac{y}{5} + 11 \) → not equivalent.

The correct answer is B. \( x = \frac{y + 11}{5} \).

Answer 2

Charity is buying peaches at the store. The cost of the peaches are $1.30 per pound. If she has $6.50 to spend on peaches, how many pounds (x) can she buy?
Set up an equation to solve the problem.
A.
1.30x=6.50
B.
1.30+x=6.50
C. 1.30/6.50=x
D.
6.50x=1.30

Answer 3

To determine how many pounds of peaches Charity can buy with her budget of $6.50 at a rate of $1.30 per pound, we can set up the following equation:

Let \( x \) be the number of pounds of peaches that Charity can buy. The cost for \( x \) pounds of peaches at $1.30 per pound is \( 1.30x \). Since she has a total of $6.50 to spend, the equation is:

\[ 1.30x = 6.50 \]

Now, let's compare this to the provided options:

A. \( 1.30x = 6.50 \) → This is correct.

B. \( 1.30 + x = 6.50 \) → This is incorrect.

C. \( \frac{1.30}{6.50} = x \) → This is incorrect.

D. \( 6.50x = 1.30 \) → This is incorrect.

The correct answer is A. \( 1.30x = 6.50 \).

Answer 4

A student solved an equation, as shown below.
The first line shows 1 over 4 left Parenthesis 8 minus 12x right parenthesis equals x minus 2 left parenthesis 2x plus 1 right parenthesis, second line shows 2 minus 3x equals x minus 4x plus 2, third line shows 2 minus 3x equals 3x plus 2, fourth line shows 2 minus 3x plus 3x equals negative 3x plus 3x plus 2. Fifth line shows 2 equals 2.

Based on the student's work, complete the statement below.

Use the drop-down menus to make the statement below true.

The student solved the equation (response area)
incorrectly
correctly
because the original equation has (response area)
no soultion
one solution
infiately many solutions

Answer 5

Based on the student's work, the key point to note is found in the last line: "2 = 2". This implies that the equation is always true regardless of the value of \( x \). This means that there are infinitely many solutions to the equation because every value of \( x \) will satisfy the equation.

Thus, you can complete the statement as follows:

The student solved the equation correctly because the original equation has infinitely many solutions.

Answer 6

Jackson solved the problem 3x-8=2(2x-7) using the following steps:
STEP 1: Use Distributive Property to get 3x-8=4x-14
STEP 2: Use Addition Property of Equality to get 3x = 4x-14+8
STEP 3: Combine Like Terms to get 3x = 4x-6
STEP 4: Use Subtraction Property of Equality to get 3x-4x= -6
STEP 5: Combine Like Terms to get (-x)=-6
What is the last step?
A.
Use Property of Equality to get x= (-6)
B.
Divide both sides by -1 to get x=6
C.
Divide both sides by -1 to get x= (-6)
D.
Use Multiplication Property of Equality to get x=6

Answer 7

After Step 5, where Jackson has arrived at the equation \(-x = -6\), the next step would be to solve for \(x\).

To solve for \(x\), you can divide both sides of the equation by \(-1\). This will yield:

\[ x = 6 \]

Now, let's evaluate the answer options:

A. Use Property of Equality to get \(x = -6\) → incorrect.

B. Divide both sides by \(-1\) to get \(x = 6\) → correct.

C. Divide both sides by \(-1\) to get \(x = -6\) → incorrect.

D. Use Multiplication Property of Equality to get \(x = 6\) → technically correct, but not specific as it doesn't mention division by \(-1\).

The best choice that accurately describes the last step is B. Divide both sides by -1 to get x=6.

Answer 8

A computer technician charges a fixed amount for a repair, plus an additional amount per hour. The equation below describes y, the total amount the technician charges, in dollars, based on x hours for the repair.

What is the meaning of the initial amount for the equation?

A.
It means the technician charges $45 per hour for the repair.

B.
It means the technician charges a fixed amount of $45 for the repair.

C.
It means the technician charges a fixed amount of $75 for the repair.

D.
It means the technician charges $75 per hour for the repair.

Answer 9

To determine the meaning of the initial amount in the equation \( y = mx + b \), where \( m \) represents the variable cost per hour and \( b \) represents the fixed amount (initial charge), we need to identify what this fixed amount is in the context of the technician's charges.

Given the options and typical interpretations of such equations:

• The initial amount \( b \) (which is often shown as a constant term) indicates the fixed charge for the repair work done before considering the hours worked.

Since none of the options provided specifically mention both the fixed charge and the variable hourly rate, we focus on the concrete fixed amount represented by the options.

Without knowing the specific equation, if we assume that \( b = 45 \), it would suggest that the technician charges $45 as a fixed fee. However, if the fixed amount is represented as $75 in the context, then the correct interpretation would be:

C. It means the technician charges a fixed amount of $75 for the repair.

If you have the specific equation or fixed amount, feel free to provide that for more precise assistance!

Answer 10

What is the first step to solve the inequality x-5<x/6

A.
Divide both sides of the inequality by 6 to simplify: x/6 - 5/6<6
B.
Divide both sides of the inequality by x to simplify: 1-5/x<6
C.
Multiply both sides of the inequality by x to simplify: x-5 < 6
D.
Multiply both sides of the inequality by 6 to simplify: 6x-30 < x

Answer 11

To solve the inequality \( x - 5 < \frac{x}{6} \), let's first determine the best first step among the options provided.

1. Rearranging the Inequality: To isolate \( x \), we can eliminate the fraction on the right side of the inequality.

Given the inequality: \[ x - 5 < \frac{x}{6} \]

To eliminate the fraction, a common approach is to multiply both sides of the inequality by 6, which is Option D:

D. Multiply both sides of the inequality by 6 to simplify: \( 6(x - 5) < x \).

When you multiply it out, you get: \[ 6x - 30 < x \]

Thus, the first step to solve the inequality \( x - 5 < \frac{x}{6} \) is:

D. Multiply both sides of the inequality by 6 to simplify: \( 6x - 30 < x \).