Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 10: Solving Equations and Inequalities 127

Undo the multiplication by dividing both sides by -3. When that’s cleared, you won’t need the

parentheses anymore.

Then add 1 to both sides to find the value of x.

Check the solution. If x is 10 and you subtract 1, you have 9, and 9 times -3 is -27. The solution of

x = 10 is correct.

()

()

31 27

31

3

27

3

19

x

x

x

5

5 -

• 
  
  
  
  • 
    
    
    
    • 52
    
    
    
    
  
  
  
  

2 -

2

x

x

19

11

10

5

51

52

1

CHECK POINT

Solve each equation.

6. 9x – 7 = -43


7. y
   11

51  1

8. 6 + 4x = 34

9.

t 3

5

 12 

10. 7(x + 5) = 119

Variables on Both Sides

The basic technique for solving an equation is to do the opposite arithmetic operation to undo

what’s been done to the variable. When there are two steps, you undo them in the opposite order.

Those rules are almost all you need to solve equations. The one piece that’s left is how to deal

with variables on both sides of the equation.

Until now, all the equations you were asked to solve had a single number, a constant, on one side.

The other side had the variable and whatever was going on, and you knew you had to undo what

was going on to get that variable all alone. But what if both sides of the equation had a variable?

What if you had to solve 7x – 4 = 5x + 2? You still need to isolate the variable, but which one?

It’s not enough to get one of the x’s all alone. If you still have an x on the other side, you won’t

know what number x represents. The key to solving an equation with variables on both sides is to

eliminate one variable term first. You can eliminate either variable term. The choice is yours.