Algebra Know-It-ALL

626 Worked-Out Solutions to Exercises: Chapters 11 to 19

Multiplying through by 4, we get

2 x+ 8 =− 4

Subtracting 8 from each side gives us

2 x=− 12

Dividing through by 2 produces

x=− 6

7. If we call the unknown number x, then we have the following equation to solve:

(x−x/10)/2 = 135

Multiplying through by 2 gives us

x−x/10= 270

Note that x−x/10 is the same as x− (1/10)x, or (9/10)x. So we have

(9/10)x= 270

Multiplying through by 10/9 gives us

(10/9)(9/10)x= 10/9 × 270

which simplifies to

x= 300

8. Let’s call Bonnie’s weight, in kilograms (kg), the unknown x. Then Bruce’s weight in
   kilograms is x+ 5, and Bill’s weight in kilograms is (x+ 5) + 10, or x+ 15. The total
   weight is 200 kg. We can now write the equation

x+ (x+ 5) + (x+ 15) = 200

Applying the commutative law and adding the constants on the left side gives us

x+x+x+ 20 = 200

which simplifies to

3 x+ 20 = 200