Linear equations in one variable
Most SAT linear-equation questions reduce to simplifying first, then using inverse operations to isolate the variable.
Core Idea
Solving a linear equation means isolating the variable by performing the same operation on both sides until you reach the form
Understanding
Linear equations in one variable usually come down to one goal: get the variable alone on one side.
- First, simplify. Distribute parentheses and combine like terms on each side before you start solving.
- Then isolate the variable. Undo addition/subtraction before multiplication/division, and keep both sides balanced.
- For word problems, translate first. Define the variable, write the equation from the context, solve, and then check that the answer makes sense in the situation.
Concept Guides
6Solve one-step and multistep linear equations in one variable.
Use inverse operations in reverse order to isolate the variable, then check your answer.
Simplify expressions using combining like terms and the distributive property.
Distribute first, then combine like terms to simplify an expression before solving.
Solve equations with variables on both sides.
Move variable terms to one side, constants to the other, and watch for no-solution or infinitely-man
Interpret coefficients, constants, terms, factors, and solutions.
Coefficients represent rates, constants represent fixed values, and the solution tells you what the
Create linear equations from a context/word problem and interpret the solution.
Translate the situation into an equation, solve it, and interpret the result in context.
Check a solution by substitution.
Substitute the proposed value into the original equation and check whether both sides are equal.