Certainly! Let's solve the equation step-by-step:
Given the equation:
[tex]\[ 2x - 3(4x - 1) = 17 + 3x \][/tex]
First, distribute the [tex]\(-3\)[/tex] on the left side:
[tex]\[ 2x - 3 \cdot 4x + 3 \cdot 1 = 17 + 3x \][/tex]
[tex]\[ 2x - 12x + 3 = 17 + 3x \][/tex]
Combine like terms on the left side:
[tex]\[ (2x - 12x) + 3 = 17 + 3x \][/tex]
[tex]\[ -10x + 3 = 17 + 3x \][/tex]
Next, isolate the variable [tex]\( x \)[/tex] by moving all [tex]\( x \)[/tex] terms to one side of the equation. Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[ -10x + 3 - 3x = 17 + 3x - 3x \][/tex]
[tex]\[ -13x + 3 = 17 \][/tex]
Now, subtract 3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -13x + 3 - 3 = 17 - 3 \][/tex]
[tex]\[ -13x = 14 \][/tex]
Finally, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\(-13\)[/tex]:
[tex]\[ x = \frac{14}{-13} \][/tex]
[tex]\[ x = -\frac{14}{13} \][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = -\frac{14}{13} \][/tex]
