Products and Ratios 197Table 12-6. Process for solving the equation 4x= 0.Statements Reasons
4 x= 0 This is the equation we are given
4 x/4= 0/4 Divide each side through by 4
x= 0 Simplify each side
Table 12-7. Process for solving the equation x/ 7 = 2.Statements Reasons
x/7= 2 This is the equation we are given
7 x/7= 7 × 2 Multiply each side by 7
x= 14 Simplify each side
Table 12-8. Process for solving the equation 2x/a=b,provided a≠ 0.Statements Reasons
2 x/a=b This is the equation we are given
a(2x/a)=ab Multiply each side by a
2 x=ab Simplify the left side
2 x/2=ab/2 Divide each side by 2
x=ab/2 Simplify the left side
Table 12-9. Process for solving the equation 5abx=c, provided a≠ 0
andb≠ 0.Statements Reasons
5 abx=c This is the equation we are given
Require that We are about to divide through by
a≠ 0 and b≠ 0 the product of these constants
Consider (5ab) to be a single constant This will allow us to solve the equation in
a “streamlined” fashion
5 abx/(5ab)=c/(5ab) Divide through by the constant (5ab)
x=c/(5ab) Simplify the left side
Table 12-10. Process for solving the equation 3x/(4a)= 3, provided a≠ 0.Statements Reasons
3 x/(4a)= 3 This is the equation we are given
Consider (4a) to be a single constant This will allow us to solve the equation
in a “streamlined” fashion
3x/(4a)= 3 × (4a) Multiply through by the constant (4a)
3 x= 12 a Simplify both sides
(3x)/3= 12 a/3 Divide each side by 3
x= 4 a Simplify each side