Compare Solution Methods for Multi-Step Equations Quick Check

Question

10f5 i
One method for solving 3 (x — 4) = 18 is to first divide by 3, then add 4. Which method below
would also result in the correct answer? (1 point)

© First, distribute the 3. then add 12, and lastly divide by 3.
© First, multiply by $. then subtract 4.

© First, distribute the 3. then add 4. and lastly divide by 3.
O First, divide by 3, then subtract 4.

Answer 1

To solve the equation \(3(x - 4) = 18\), we start with the proposed method of first dividing by 3 and then adding 4.

If we divide both sides by 3: \[ x - 4 = 6 \] Then, adding 4 gives: \[ x = 10 \]

Now, let's examine the other methods listed:

1. First, distribute the 3, then add 12, and lastly divide by 3.

   • Distributing gives \(3x - 12 = 18\).
   • Adding 12 results in \(3x = 30\).
   • Dividing by 3 gives \(x = 10\). (This method works.)

2. First, multiply by \( \frac{1}{3} \), then subtract 4.

   • Multiplying by \( \frac{1}{3} \) gives \(x - 4 = 6\).
   • Subtracting 4 gives \(x = 6 + 4\), which results in \(x = 10\). (This method works.)

3. First, distribute the 3, then add 4, and lastly divide by 3.

   • Distributing gives \(3x - 12 = 18\).
   • Adding 4 results in \(3x - 8 = 18\).
   • Dividing by 3 gives \(x - \frac{8}{3} = 6\), which does not lead to the correct answer. (This method does not work.)

4. First, divide by 3, then subtract 4.

   • Dividing by 3 gives \(x - 4 = 6\).
   • Subtracting 4 gives \(x = 6 + 4\), which leads to \(x = 10\). (This method works.)

Therefore, the methods that result in the correct answer are:

• First, distribute the 3, then add 12, and lastly divide by 3.
• First, multiply by \( \frac{1}{3} \), then subtract 4.
• First, divide by 3, then subtract 4.

The only method listed that decently does lead us to the correct solution, as indicated, is the first option.

Answer 2

only one answer

Answer 3

Apologies for the confusion. The correct answer from the choices given is:

First, distribute the 3, then add 12, and lastly divide by 3.

This method correctly leads to the solution \(x = 10\).

Answer 4

When solving the equation -3(2 + 10) = —3, identify the operation that should be done first.
(1 point)
© multiply by —2
© divide by —2
© add 10
© subtract 10

Answer 5

To solve the equation \(-3(2 + 10) = -3\), you need to evaluate the expression inside the parentheses first due to the order of operations (also known as PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The operation inside the parentheses is \(2 + 10\). Therefore, the first operation that should be done is:

Add 10.

Thus, the correct answer is:

© add 10.

Answer 6

Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is
$3 less than the cost of an adult ticket. Identify the first step if solving this problem arithmetically,
which would find the cost of one adult and one child ticket. (7 point)

© Subtract 6 from 75.

© Add 3 to 75.

© Divide 75 by 3.

© Divide 75 by 6.

Answer 7

To solve the problem, let's define the variables for the costs:

• Let \( a \) be the cost of one adult ticket.
• Let \( c \) be the cost of one child ticket.

From the problem, we know:

1. The total cost for three adult tickets and three child tickets is $75: \[ 3a + 3c = 75 \]

2. The cost of each child ticket is $3 less than the cost of an adult ticket: \[ c = a - 3 \]

Next, we can simplify the equation \(3a + 3c = 75\) by dividing everything by 3: \[ a + c = 25 \]

Now substituting \(c = a - 3\) into \(a + c = 25\): \[ a + (a - 3) = 25 \] \[ 2a - 3 = 25 \]

Now, to find the first step arithmetically, we want to isolate the term involving \(a\). The first logical step here would be to add 3 to both sides of the equation from the simplified version: \[ a + c = 25 \]

This leads to: \[ a + (a - 3) = 25 \]

Thus, the first step to find \(a\) and \(c\) after substituting is to add 3 to 25. However, let’s look at your answer choices to find what corresponds best.

Based on your answer choices, the most suitable first operational approach would be adding 3:

• © Add 3 to 75.

This is indirectly asking for an operation related to finding \(a\) from \(c = a - 3\).

So the best choice reflecting a first logical step in solving for either ticket would be:

© Add 3 to 75.

Answer 8

Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is
$3 less than the cost of an adult ticket. The first step to solving this problem algebraically is to write
an equation: 3 (a + 2 — 3) = 75, where x represents the cost of an adult ticket. Identify the next
step, which would simplify the equation before solving for the variable. (7 point)

© Divide 75 by 3.

© Combine like terms in parentheses.

© Add 3 to 75

© Distribute values over the variables.

Answer 9

The equation provided is:

\[ 3(a + 2 - 3) = 75 \]

To simplify this equation before solving for the variable, we need to look at the expression inside the parentheses.

The expression \(a + 2 - 3\) combines \(2\) and \(-3\). Therefore, the next step would be to combine the like terms in the parentheses:

\[ 2 - 3 = -1 \]

So, it simplifies to:

\[ 3(a - 1) = 75 \]

Therefore, the correct step to take next is:

© Combine like terms in parentheses.