Solve for x: 5.6 - (x times 13 divided by 4 - 1 and 5/6 times x) divided by 17 times 3 = 13 divided by 5.

Step-by-step solution

1. 1

   Convert every number to a fraction before touching the algebra. Mixed numbers and decimals in the same expression are the main source of error here:

   $1\tfrac{5}{6}=\frac{11}{6},\qquad 5.6=\frac{28}{5},\qquad \frac{13}{5}=2.6.$

2. 2

   Combine the two x-terms inside the bracket. The common denominator of $4$ and $6$ is $12$:

   $\frac{13x}{4}-\frac{11x}{6}=\frac{39x}{12}-\frac{22x}{12}=\frac{17x}{12}.$

   The numerator $17$ appearing here is not a coincidence — it is about to cancel the divisor.

3. 3

   Apply the division and multiplication left to right. Dividing by $17$ and multiplying by $3$:

   $\frac{17x}{12}\div 17\times 3=\frac{x}{12}\times 3=\frac{x}{4}.$

   The whole middle of the expression has collapsed to a single quarter of $x$.

4. 4

   Rewrite and solve the resulting one-step equation.

   $\frac{28}{5}-\frac{x}{4}=\frac{13}{5}\ \Longrightarrow\ \frac{x}{4}=\frac{28-13}{5}=\frac{15}{5}=3\ \Longrightarrow\ x=12.$

5. 5

   Substitute back into the original expression. With $x=12$: the bracket is $\tfrac{13\cdot 12}{4}-\tfrac{11\cdot 12}{6}=39-22=17$; then $17\div 17\times 3=3$; and $5.6-3=2.6=\tfrac{13}{5}$ ✓.