Basic Equation Solving
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Algebra
Summary
Basic equation solving on the ACT focuses on isolating the variable while keeping the equation balanced. The most effective strategy is to reverse the order of operations rather than perform random allowable operations.
- Equation solving differs from rewriting algebraic expressions because the goal is to find the specific value of the variable, not just create an equivalent form.
- The key rule is balance: whatever operation is applied to one side of the equation must also be applied to the other side.
- Not every mathematically allowed step is strategically useful; strong solving choices reverse the order of operations acting on the variable.
- For equations like 3x + 5 = 17, subtract the constant first and then divide, since dividing too early can create unnecessary fractions.
- A helpful way to remember the strategy is that undoing happens in reverse order, just like taking off shoes before socks.
- When the variable appears on both sides, move all variable terms to one side and all constants to the other before isolating the variable.
- These methods apply to linear equations, where the highest power of x is 1; different rules are needed for non-linear equations.
Chapters
00:00
From Equivalent Expressions to Solving for a Variable
00:57
Balancing Equations and Choosing Strategic Moves
02:26
Undoing the Order of Operations
03:05
Why Subtract Before Dividing
04:33
Handling Variables on Both Sides and Linear Equations