Let's solve the equation step by step to understand the process clearly. We need to solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ 3x + 4 = 10 \][/tex]
1. Subtract 4 from both sides to isolate the term with the variable:
[tex]\[ 3x + 4 - 4 = 10 - 4 \][/tex]
This simplifies to:
[tex]\[ 3x = 6 \][/tex]
2. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{6}{3} \][/tex]
So we find:
[tex]\[ x = 2 \][/tex]
Now, referring to the multiple-choice options, which involves transposing terms, we can look for an equivalent transformation:
a) [tex]\(-4 = 10 - 3x\)[/tex] (Let's test if this is valid)
Subtracting 4 from both sides of the original equation does not directly lead to this form.
b) [tex]\(4 = 3x + 10\)[/tex] (This is a rearrangement of the original equation, but does not help with solving it)
c) [tex]\(4 = -3x + 10\)[/tex] (This form implies adding the variable term to both sides incorrectly)
d) [tex]\(-4 = -3x\)[/tex] (Let's check if this is true)
By transposing [tex]\(3x\)[/tex] to the right-hand side of [tex]\(3x = 6\)[/tex]:
[tex]\[ 10 - 4 = 6 \quad \text{(which is a standard arithmetic operation)} \][/tex]
Subtracting [tex]\(3x\)[/tex] from both sides gives:
[tex]\[ -4 = -3x \][/tex]
This matches our given equation perfectly.
Therefore, the correct answer is:
d) [tex]\(-4 = -3x\)[/tex]
