Let's analyze the steps to solve the equation [tex]\(6x - 4 = 8\)[/tex].
Step 1: Add 4 to both sides of the equation to isolate the term with [tex]\(x\)[/tex].
[tex]\[ 6x - 4 + 4 = 8 + 4 \][/tex]
This is justified by the addition property of equality, which states that adding the same value to both sides of an equation maintains equality.
Step 2: Simplify the expression by combining like terms on both sides.
[tex]\[ 6x + 0 = 12 \][/tex]
Here, [tex]\(-4 + 4\)[/tex] on the left side simplifies to 0.
Step 3: Simplify further to:
[tex]\[ 6x = 12 \][/tex]
The property that justifies this step is the identity property of addition. The identity property of addition states that any number plus zero is the number itself, so [tex]\(6x + 0\)[/tex] simplifies to [tex]\(6x\)[/tex].
Step 4: Divide both sides by 6 to solve for [tex]\(x\)[/tex].
[tex]\[ \frac{6x}{6} = \frac{12}{6} \][/tex]
This is based on the multiplication property of equality, which allows you to divide both sides of an equation by the same nonzero number.
Step 5: Simplify the fractions.
[tex]\[ x = 2 \][/tex]
Step 6: The final solution is:
[tex]\[ x = 2 \][/tex]
In conclusion, Step 3 is justified by the identity property of addition.
