THREE-STEP EQUATIONS

 Sometimes we need to take three steps to solve an equation. But it still just a matter of mental arithmetic.

Solve 3x /5 + 4 = 10.

 First 10 – 4 = 6, 

then 6×5 = 30, 

then 30÷3 = 10 

so x = 10. 

Solve 3x + 2 /4 = 8.

 First 8×4 = 32,

 then 32–2 = 30,

 then 30÷3 = 10 

so x = 10

Solve 2(3x + 4) = 38. 

The bracket here indicates that 3x + 4 is being multiplied by the number outside the bracket, which is 2.

 So we begin by dividing 38 by 2. 

First 38 ÷ 2 = 19, 

then 19 – 4 = 15, 

then 15 ÷ 3 = 5

 so x = 5.

 Alternatively, 

here, we can multiply the bracket out first: If 2(3x + 4) = 38 then 

6x + 8 = 38 and 

so 38 – 8 = 30 and 

30 ÷ 6 = 5. 

Practice C Solve the following mentally: 

1.  2x /3 + 4 = 8 
2.  3x /5 – 4 = 5
3.   7x /2 – 10 = 11 
4.  3x /8 +17 = 20 
5.  2x +1 / 3  = 4
6.   2x - 3 /5  = 3 
7.  5x +2/ 3 = 9 
8.  6x -1 /7 = 5 
9.  3(5x – 2) = 54 
10.  8(x + 3) = 64 
11.  3(7x – 3) = 33
12.   2( 4x + 3) = 102