solve for x. 15 - x + 3 = 17 - 3x. write the exact answer using either base - 10 or base - e logarithms.

Explanation:

Step1: Simplify the equation

First, simplify the given equation $15 - x+3=17 - 3x$. Combine like - terms on the left - hand side: $18 - x=17 - 3x$.

Step2: Add $3x$ to both sides

Add $3x$ to both sides of the equation to get all $x$ terms on one side: $18 - x+3x=17 - 3x+3x$, which simplifies to $18 + 2x=17$.

Step3: Subtract 18 from both sides

Subtract 18 from both sides: $18 + 2x-18=17 - 18$, resulting in $2x=-1$.

Step4: Solve for $x$

Divide both sides by 2: $x =-\frac{1}{2}$.

Answer:

$x =-\frac{1}{2}$