Marlena solved the equation 2x + 5 = –10 – x. Her steps are shown below.

Question

2x + 5 = –10 – x

3x + 5 = –10
3x = –15
x = –5
Use the drop-down menus to justify Marlena’s work in each step of the process.

Step 1:

Step 2:

Step 3:

Answer 1

Here’s a justification for each step of Marlena’s work:

Step 1: (Original Equation)
Justification: This is the original equation.
(2x + 5 = -10 - x)

Step 2: (Add x to both sides)
Justification: Add x to both sides to combine like terms.
(2x + x + 5 = -10 - x + x) reduces to 3x + 5 = -10

Step 3: (Subtract 5 from both sides)
Justification: Subtract 5 from both sides to isolate the term with x.
(3x + 5 - 5 = -10 - 5) simplifies to 3x = -15

Step 4: (Divide by 3)
Justification: Divide both sides by 3 to solve for x.
(3x/3 = -15/3) results in x = -5

You can use these justifications to fill the drop-down menus as appropriate for each step of Marlena's process.

Answer 2

step 1 and 3 answers are addition property of equality or multiplication property of equality or combined like terms.
and for step 2 its either subtraction property of equality or division property of equality and combined like terms

only one answer of each step is correct

Answer 3

Thank you for the clarification! Here are the appropriate justifications based on the properties of equality:

Step 1:
Justification: This is the original equation.

Step 2:
Justification: Combined like terms.
(2x + 5 = -10 - x changes to 3x + 5 = -10)

Step 3:
Justification: Subtraction property of equality.
(3x + 5 - 5 = -10 - 5 simplifies to 3x = -15)

In this format, each step has a single justification.

Answer 4

okay wait i dont get 1 and 3
you ANSWERED 2 combined like terms but what about those 2??
the answers for step 1 that YOU MUST CHOOSE ARE addition property of equality or multiplication property of equality or combined like terms.
and FOR STEP 3 addition property of equality or multiplication property of equality or combined like terms.

Answer 5

I apologize for the misunderstanding! Thank you for clarifying the choices for justification. Here are the correct justifications for each step based on your options:

Step 1: Justification: Addition property of equality.
(This is because we will eventually add \( x \) to both sides in the next step.)

Step 2: Justification: Combined like terms.
(Combining \( 2x \) and \( -x \) leads to \( 3x \).)

Step 3: Justification: Subtraction property of equality.
(Subtracting 5 from both sides leads to \( 3x = -15 \).)

Please let me know if you need further assistance!

Answer 6

STEP 2 AND STEP 3 WERE NOT CORRECT BUT WHAT IS THE ANSWER FOR 2?? ITS NOT COMBINED TERMS

Answer 7

Thank you for your patience. Here’s the corrected justification for each step based on the options provided:

Step 1:
Justification: Addition property of equality.
(This is because we will eventually add \( x \) to both sides in the next step.)

Step 2:
Justification: Subtraction property of equality.
(Here, adding \( x \) to both sides results in \( 3x + 5 = -10. \))

Step 3:
Justification: Subtraction property of equality.
(Here, subtracting \( 5 \) from both sides results in \( 3x = -15. \))

So, for Step 2, the correct answer would be Subtraction property of equality. Thank you for pointing that out, and sorry for the confusion!

Answer 8

OKAY FOR THE PEOPLE WHO NEED HELP
Step 1: addition property of equality

Step 2: subtraction property of equality

Step 3: division property of equality

now What can each term of the equation be multiplied by to eliminate the fractions before solving?

x – + 2x = StartFraction one-half EndFraction x minus StartFraction 5 Over 4 EndFraction plus 2 x equals StartFraction 5 Over 6 EndFraction plus x. + x

2
6
10
12

Answer 9

To eliminate the fractions from the equation

\[ x + 2x = \frac{1}{2}x - \frac{5}{4} + 2x = \frac{5}{6} + x \]

you need to find the least common multiple (LCM) of the denominators. The denominators present in the equation are:

• 2
• 4
• 6

The LCM of these numbers is 12. Therefore, to eliminate the fractions, you can multiply every term in the equation by 12.

Thus, the answer is 12.