The option that has the correction justifications is the fourth option --- 1. Multiplication property of equality 2. Combine like terms 3. Addition property of equality 4. Division property of equality
From the question, we are to determine which of the given options has the correct justifications
To do this, we will solve the equation as well
The given equation is
x + 1/2(6x - 4) = 6
Multiply through by 2
2×x + 2×1/2(6x - 4) = 2×6
2x + (6x - 4) = 12
2x + 6x - 4 = 12
Combine like terms
8x - 4 = 12
Add 4 to both sides of the equation
8x - 4 + 4 = 12 + 4
8x = 16
Divide both sides of the equation by 8
8x/8 = 16/8
x = 2
From above, we can observe that the justifications used are
Multiplication property of equality
Combine like terms
Addition property of equality
Division property of equality
Hence, the option that has the correction justifications is the fourth option --- 1. Multiplication property of equality 2. Combine like terms 3. Addition property of equality 4. Division property of equality
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Answer:
1. Multiplication property of equality
2. Combine like terms
3. Addition property of equality
4. Division property of equality
Step-by-step explanation:
Given equation:
[tex]x+\dfrac{1}{2} (6x-4) = 6[/tex]
Wyatt's Step Work:
[tex]\textsf{1.} \quad 2x + 6x-4 = 12[/tex]
[tex]\textsf{2.} \quad 8x-4 = 12[/tex]
[tex]\textsf{3.} \quad 8x = 16[/tex]
[tex]\textsf{4.} \quad x = 2[/tex]
Step 1
Wyatt multiplied both sides of the equation by 2.
Multiplication property of equality: When both sides of an equation are multiplied by the same number, the two sides remain equal.
Step 2
Wyatt added the terms with the variable x.
Combine like terms: When one term is made by adding/subtracting the coefficients and keeping the variables the same.
Step 3
Wyatt added 4 to both sides of the equation.
Addition property of equality: When the same number is added to both sides of an equation, the two sides remain equal.
Step 4
Wyatt divided both sides of the equation by 8.
Division property of equality: When both sides of an equation are divided by the same number, the two sides remain equal.
