Sure, let's solve the equation step by step to find the correct value of [tex]\( x \)[/tex].
The given equation is:
[tex]\[ -3x + 1 + 10x = x + 4 \][/tex]
Step 1: Combine like terms on the left side of the equation.
[tex]\[ -3x + 10x + 1 = x + 4 \][/tex]
[tex]\[ 7x + 1 = x + 4 \][/tex]
Step 2: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constant terms to the other side. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ 7x + 1 - x = x + 4 - x \][/tex]
[tex]\[ 6x + 1 = 4 \][/tex]
Step 3: Isolate the term with [tex]\( x \)[/tex]. Subtract 1 from both sides:
[tex]\[ 6x + 1 - 1 = 4 - 1 \][/tex]
[tex]\[ 6x = 3 \][/tex]
Step 4: Solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[ x = \frac{3}{6} \][/tex]
[tex]\[ x = \frac{1}{2} \][/tex]
So, the solution for the equation is:
[tex]\[ x = \frac{1}{2} \][/tex]
Therefore, the correct option is:
[tex]\[ x = \frac{1}{2} \][/tex]
