Solve the equation negative 4 times (negative 11 plus 5x) plus 6 times (26 minus 6x) equals negative 3 times (4x plus 1) plus 5 times (11 plus 6x).

Step-by-step solution

1. 1

   Expand the left-hand side, tracking every sign. A negative multiplier in front of a bracket that already contains a negative is the classic place to slip:

   $-4(-11+5x)=44-20x$

   $6(26-6x)=156-36x$

   Adding them:

   $\text{LHS}=44-20x+156-36x=200-56x$

2. 2

   Expand the right-hand side the same way.

   $-3(4x+1)=-12x-3$

   $5(11+6x)=55+30x$

   Adding them, and combining $-12x$ with $+30x$:

   $\text{RHS}=-12x-3+55+30x=18x+52$

   It is worth pausing here: $-12+30=18$, not $22$. Mis-adding these two coefficients is the single most common error in this problem.

3. 3

   Write the simplified equation.

   $200-56x=18x+52$

4. 4

   Gather like terms. Add $56x$ to both sides and subtract $52$ from both sides:

   $200-52=18x+56x$

   $148=74x$

5. 5

   Divide and simplify.

   $x=\frac{148}{74}=2$

6. 6

   Substitute $x=2$ into the original equation. Left side:

   $-4(-11+10)+6(26-12)=-4(-1)+6(14)=4+84=88$

   Right side:

   $-3(8+1)+5(11+12)=-27+115=88$

   Both sides are $88$, so $x=2$ is confirmed. The equation does have a solution — the no solution option offered on this exercise is a distractor.