Cafeteria Actions and Reactions

Learning Focus

Solve equations by balancing: do the same operation to both sides to keep equality.

Big idea

An equation is like a balanced scale. Any operation applied to both sides keeps it balanced:

• Add or subtract the same quantity (including variable terms).
• Multiply or divide both sides by the same nonzero number.
• Distribute and combine like terms first when needed.

Goal: isolate the variable.

Worked example

Solve $3x+5=2x+12$.

• Subtract $2x$: $x+5=12$
• Subtract $5$: $x=7$
• Check: $3(7)+5=26$ and $2(7)+12=26$ ✓

Solve $5(x-2)=3x+4$: $5x-10=3x+4\Rightarrow2x=14\Rightarrow x=7$.

Takeaways

• Do the same thing to both sides.
• Move variable terms to one side, constants to the other.
• Always check by substituting.