Let's solve the given equation step-by-step:
Given equation:
[tex]\[ -3x + 1 + 10x = x + 4 \][/tex]
First, combine like terms on the left-hand side:
[tex]\[ (-3x + 10x) + 1 = x + 4 \][/tex]
[tex]\[ 7x + 1 = x + 4 \][/tex]
Next, subtract [tex]\(x\)[/tex] from both sides to get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 7x + 1 - x = 4 \][/tex]
[tex]\[ 6x + 1 = 4 \][/tex]
Now, subtract 1 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 6x + 1 - 1 = 4 - 1 \][/tex]
[tex]\[ 6x = 3 \][/tex]
Finally, divide both sides by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{3}{6} \][/tex]
[tex]\[ x = \frac{1}{2} \][/tex]
So, the solution to the equation [tex]\(-3x + 1 + 10x = x + 4\)[/tex] is:
[tex]\[ x = \frac{1}{2} \][/tex]
The correct option from the given choices is:
[tex]\[ x = \frac{1}{2} \][/tex]
