Algebra Know-It-ALL

200 First-Degree Equations in One Variable

Table 12-13. Streamlined process for solving

the equation a− 3 x= 0.

Statements Reasons

a− 3 x= 0 This is the equation we are given

− 3 x=−a Subtract a from each side

3 x=a Multiply through by − 1

x=a/3 Divide through by 3

Table 12-14. Streamlined process for solving

the equation a− 5 + 15 x= 0.

Statements Reasons

a− 5 + 15 x= 0 This is the equation we are given

− 5 + 15 x=−a Subtract a from each side

15 x=−a+ 5 Add 5 to each side

15 x= 5 −a Commutative law for addition; change

negative addition to subtraction

x= (5 −a)/15 Divide through by 15

x= 5/15 −a/15 Right-hand distributive law for division over

subtraction

x= 1/3 −a/15 Reduce the numerical fraction to lowest terms

Table 12-15. Streamlined process for solving

the equation a− 8 x=b.

Statements Reasons

a− 8 x=b This is the equation we are given

− 8 x=b−a Subtract a from each side

−x= (b−a)/8 Divide through by 8

x=−(b−a)/8 Multiply through by − 1

x= (a−b)/8 Simplify the right side

x=a/8−b/8 Right-hand distributive law for division over

subtraction

Table 12-16. Streamlined process for solving

the equation − 6 a+ 3 x= 12 b.

Statements Reasons

− 6 a+ 3 x= 12 b This is the equation we are given

3 x= 6 a+ 12 b Add 6a to each side

x= (6a+ 12 b)/3 Divide through by 3

x= 2 a+ 4 b Right-hand distributive law for division over

addition