Solve 3(x - 3) = 5 - 2(2 - 5x) for x.

Step-by-step solution

1. 1

   Expand the left side.

   $3(x-3)=3x-9$

2. 2

   Expand the right side, watching the double negative. The $-2$ multiplies both terms inside:

   $-2(2-5x)=-4+10x$

   The second product is $(-2)(-5x)=+10x$. Writing $-10x$ here is the error that derails this problem.

3. 3

   Simplify the right side.

   $5-4+10x=1+10x\quad\Rightarrow\quad 3x-9=1+10x$

4. 4

   Collect the terms. Subtract $3x$ from both sides, then subtract $1$:

   $-9=1+7x\quad\Rightarrow\quad -10=7x$

   Moving the smaller $x$ term keeps the coefficient positive.

5. 5

   Divide and check exactly.

   $x=-\frac{10}{7}\approx -1.4286$

   Check: the left side is $3\left(-\frac{10}{7}-3\right)=3\left(-\frac{31}{7}\right)=-\frac{93}{7}$, and the right side is $5-2\left(2+\frac{50}{7}\right)=5-2\cdot\frac{64}{7}=5-\frac{128}{7}=-\frac{93}{7}$ ✓.