Question

7. Which equation has the same first step to solve as this equation: 2x+12−3x=27
(1 point)
Responses

2x+12=−3x−27
2 x plus 12 is equal to negative 3 x minus 27

2(x−5)+2x=10
2 times open paren x minus 5 close paren plus 2 x is equal to 10

2x+12=27
2 x plus 12 is equal to 27

4x−17+2x=9
4 x minus 17 plus 2 x is equal to 9
Question 3
8. Using the Distributive Property as a good first step to solving the equation 7(5x+2)=−4(6−5x)
, you could simplify this equation to get which of these choices?(1 point)
Responses

35x+14=−24+20x
35 x plus 14 is equal to negative 24 plus 20 x

5x+14=6+20x
5 x plus 14 is equal to 6 plus 20 x

35x+2=−24−5x
35 x plus 2 is equal to negative 24 minus 5 x

35x+14=−24−20x
35 x plus 14 is equal to negative 24 minus 20 x

35x+2=24−20x

Answer 1

For Question 7, we start with the equation:

\[ 2x + 12 - 3x = 27 \]

The first step in solving this equation is to combine like terms on the left side. This looks like:

\[ (2x - 3x) + 12 = 27 \]

This can be written as:

\[ -x + 12 = 27 \]

Now let's evaluate the provided options based on what has the same first step (combining like terms):

1. **Option 1:** \( 2x + 12 = -3x - 27 \) (not the same first step)
2. **Option 2:** \( 2(x - 5) + 2x = 10 \) (not the same first step, requires distribution)
3. **Option 3:** \( 2x + 12 = 27 \) (same first step; we can directly combine)
4. **Option 4:** \( 4x - 17 + 2x = 9 \) (not the same first step)

The correct answer for Question 7 is **Option 3: \( 2x + 12 = 27 \)**.

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For Question 8, we start with the equation:

\[ 7(5x + 2) = -4(6 - 5x) \]

Using the Distributive Property, we expand both sides:

Left side:
\[ 7(5x + 2) = 35x + 14 \]

Right side:
\[ -4(6 - 5x) = -24 + 20x \]

Thus, we can simplify the original equation to:

\[ 35x + 14 = -24 + 20x \]

Now let's evaluate the options provided:

1. **Option 1:** \( 35x + 14 = -24 + 20x \) (this is correct)
2. **Option 2:** \( 5x + 14 = 6 + 20x \) (not correct)
3. **Option 3:** \( 35x + 2 = -24 - 5x \) (not correct)
4. **Option 4:** \( 35x + 14 = -24 - 20x \) (not correct)
5. **Option 5:** \( 35x + 2 = 24 - 20x \) (not correct)

The correct answer for Question 8 is **Option 1: \( 35x + 14 = -24 + 20x \)**.