Solve (7.26 − x)/4.51 + 2.18 × (8.79x + 7.37) = (3.84x + 28.32)/6.45, giving x correct to two decimal places.

Step-by-step solution

1. 1

   Split the left-hand fraction. Dividing each term of the numerator separately turns it into a constant plus a multiple of $x$; note the $-x$ produces a negative coefficient:

   $\frac{7.26-x}{4.51}=\frac{7.26}{4.51}-\frac{1}{4.51}x=1.609756-0.221729x$

2. 2

   Expand the product.

   $2.18\times 8.79=19.1622,\qquad 2.18\times 7.37=16.0666$

   so the second term is $19.1622x+16.0666$.

3. 3

   Split the right-hand fraction.

   $\frac{3.84x+28.32}{6.45}=0.595349x+4.390698$

4. 4

   Collect the x terms on the left and the constants on the right.

   $-0.221729x+19.1622x-0.595349x=4.390698-1.609756-16.0666$

   $18.345122x=-13.285658$

5. 5

   Divide and round.

   $x=\frac{-13.285658}{18.345122}=-0.724207\approx -0.72$

   $\boxed{x=-0.72}$

6. 6

   Check by substitution. With $x=-0.724207$: the left side is $\tfrac{7.984207}{4.51}+2.18(1.004220)=1.770334+2.189201=3.959535$, and the right side is $\tfrac{-2.780955+28.32}{6.45}=\tfrac{25.539045}{6.45}=3.959542$ — agreeing to five decimal places, the residual coming only from the six-decimal rounding of the intermediates.