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Which of the following equations is equivalent to 4x + 6 = 1?

• A. 1 + 3(x+2) =1
• B. 5(x + 2) - x= 1
• c. 18 + 6(x - 2) - 2x=1
• D. 9x-5(x-1) - 1= 1

9 answers

To determine which equation is equivalent to \(4x + 6 = 1\), we will transform each option and check if it simplifies to \(4x + 6 = 1\).

  1. Starting Equation: \(4x + 6 = 1\)

Next, we will solve for \(x\) in this equation:

\[ 4x = 1 - 6 \ 4x = -5 \ x = -\frac{5}{4} \]

Now let's check each option:

Option A: \(1 + 3(x + 2) = 1\)

Distributing \(3\):

\[ 1 + 3x + 6 = 1 \ 3x + 7 = 1 \ 3x = 1 - 7 \ 3x = -6 \ x = -2 \]

Not equivalent.

Option B: \(5(x + 2) - x = 1\)

Distributing \(5\):

\[ 5x + 10 - x = 1 \ 4x + 10 = 1 \ 4x = 1 - 10 \ 4x = -9 \ x = -\frac{9}{4} \]

Not equivalent.

Option C: \(18 + 6(x - 2) - 2x = 1\)

Distributing \(6\):

\[ 18 + 6x - 12 - 2x = 1 \ 4x + 6 = 1 \]

This is equivalent!

Option D: \(9x - 5(x - 1) - 1 = 1\)

Distributing \(-5\):

\[ 9x - 5x + 5 - 1 = 1 \ 4x + 4 = 1 \ 4x = 1 - 4 \ 4x = -3 \ x = -\frac{3}{4} \]

Not equivalent.

The only option that simplifies to \(4x + 6 = 1\) is:

C. \(18 + 6(x - 2) - 2x = 1\)

Albert walks
4/5 of a mile in 5/12
of an hour. Which expression can be used to calculate his unit rate in miles per hour?

A. 4/5 - 5/12

B. 5/12 x 4/5

C. 5/12/4/5

D. 4/5/5/12

To find the unit rate in miles per hour, we need to express Albert's distance traveled in miles divided by the time taken in hours.

He walked \( \frac{4}{5} \) of a mile in \( \frac{5}{12} \) of an hour. The expression for the unit rate (miles per hour) can be calculated as:

\[ \text{Unit rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{4}{5} \text{ miles}}{\frac{5}{12} \text{ hours}} \]

Dividing a fraction by another fraction is the same as multiplying by its reciprocal:

\[ \text{Unit rate} = \frac{4}{5} \div \frac{5}{12} = \frac{4}{5} \times \frac{12}{5} \]

This matches the expression in option D when we simplify it:

Thus, the right choice to calculate the unit rate in miles per hour is:

D. \(\frac{4}{5} \div \frac{5}{12} \) (which can also be expressed as \(\frac{4}{5}/\frac{5}{12}\)).

Out of the 32 students in Mr. Martin's class, 18 are boys. If this ratio is proportional to the ratio of students in the school and the number of boys in the school, which of the following proportions would best be used to find the number of students in the school? It is given that there are 468 boys in the school.

A. 18/32 = s/468

B. 32/18 = s/468

C. 468/32 = s/18

D. 32/s = 18/468

To find the number of students in the school based on the ratio of boys to the total number of students in Mr. Martin's class, we can set up a proportion that compares the ratio from the class to the ratio from the school.

In Mr. Martin's class:

  • The number of boys = 18
  • The total number of students = 32
  • The ratio of boys to total students in the class is \( \frac{18}{32} \).

In the school:

  • The number of boys = 468
  • Let \( s \) be the total number of students in the school.

We want to set up a proportion:

\[ \frac{18}{32} = \frac{468}{s} \]

This corresponds to option:

A. \( \frac{18}{32} = \frac{s}{468} \)

Thus, the correct proportion to find the number of students in the school is A.

The cost of a concert ticket last week was $60.00. This week a concert ticket is $75.00. What is the percent increase of the ticket from last week to this week?
• A.8%
) B. 15%
• c. 20%
• D. 25%

To calculate the percent increase from last week to this week, we can use the following formula:

\[ \text{Percent Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100% \]

In this case, the old value (last week's ticket price) is $60.00, and the new value (this week's ticket price) is $75.00.

Now we can plug in these values:

\[ \text{Percent Increase} = \frac{75.00 - 60.00}{60.00} \times 100% \]

Calculating the numerator:

\[ 75.00 - 60.00 = 15.00 \]

Now substituting back:

\[ \text{Percent Increase} = \frac{15.00}{60.00} \times 100% \]

Calculating the fraction:

\[ \frac{15.00}{60.00} = 0.25 \]

Now convert to a percentage:

\[ 0.25 \times 100% = 25% \]

Therefore, the percent increase of the ticket from last week to this week is D. 25%.

Which expression is equivalent to 0?
• А. (a)(—a)
• B. a + (-a)
C. a/-a
• D. a - (-a)

To determine which expression is equivalent to \(0\), let's analyze each option:

A. \((a)(-a)\)

This expression equals \(-a^2\). This is not equal to \(0\) unless \(a = 0\).

B. \(a + (-a)\)

This expression simplifies to:

\[ a - a = 0 \]

This expression is equal to \(0\).

C. \(\frac{a}{-a}\)

This expression simplifies to:

\[ -\frac{a}{a} = -1 \quad (\text{for } a \neq 0) \]

This expression is not equal to \(0\).

D. \(a - (-a)\)

This expression simplifies to:

\[ a + a = 2a \]

This expression is not equal to \(0\) unless \(a = 0\).

So, the only expression that is equivalent to \(0\) is:

B. \(a + (-a)\).