Solve the negative of (5x - 4), plus 2 times (x - 7), equals -1.

Step-by-step solution

1. 1

   Read the leading minus as multiplication by $-1$. It applies to both terms inside the bracket:

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

   The constant becomes $+4$. Writing $-5x-4$ here is the most frequent error in this type of equation.

2. 2

   Distribute the 2 over the second bracket.

   $2(x-7)=2x-14$

   so the equation reads

   $-5x+4+2x-14=-1$

3. 3

   Combine like terms.

   $-5x+2x=-3x,\qquad 4-14=-10\quad\Rightarrow\quad -3x-10=-1$

4. 4

   Isolate the $x$ term. Add $10$ to both sides:

   $-3x=9$

5. 5

   Divide by the negative coefficient and check.

   $x=\frac{9}{-3}=-3$

   Substituting back: $-(5(-3)-4)+2(-3-7)=-(-19)+2(-10)=19-20=-1$ ✓. (This is an equation, so dividing by $-3$ needs no sign flip — that rule belongs to inequalities.)