Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Solve the equation:
[tex]\[ -3x + 1 + 10x = x + 4 \][/tex]

A. [tex]\[ x = \frac{1}{2} \][/tex]

B. [tex]\[ x = \frac{5}{6} \][/tex]

C. [tex]\[ x = 12 \][/tex]

D. [tex]\[ x = 18 \][/tex]


Sagot :

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]