Solving Two-Step Equations
Read a two-step equation as a process built around x, then undo those layers with equivalent transformations until the variable is isolated.
If x is hidden behind two operations, which layer should we undo first?
Equality is still the rule: every transformation must preserve both sides. The new challenge is strategy. We usually remove the outer layer first because it keeps the arithmetic simple.
A different balanced route can still be valid even when it is not the cleanest route.
Operations wrap around x in layers.
For 3x + 5, multiplication happens to x first; addition is the outer layer that acts last.
Undo the construction in reverse.
Reverse order is a useful default because it peels away the outer operation without disturbing the inner structure.
Peel the equation back to x.
Remove the outer +5 layer.
Choose an operation to apply to the entire left side and the entire right side.
Solve first. Substitution checks the value you derived; it does not discover the value for you.
A different first step can be legal without being pleasant.
For 3x + 5 = 20, both routes below preserve the same solution. The first route is preferred because it keeps the numbers simple.
Subtract 5, then divide by 3.
Divide every term by 3 first. Equality survives, but fractions appear.