Solve equations with variables on both sides

Learning Objectives Isolate a variable in a multi-step linear equation with variables on both sides. Apply the distributive property to simplify equations before solving. Combine like terms on each side of an equation to simplify it. Solve linear equations that result in one solution, no solution, or infinitely many solutions. Translate a word problem into a linear equation with variables on both sides and solve it. Verify the solution to an equation by substituting the value back into the original equation. 🤔 Ever tried to figure out which gym membership is a better deal? Solving equations with variables on both sides is the mathematical tool you need to find the exact point where one option becomes cheaper than the other! In this tutorial, you will master the step-by-ste...

TermDefinitionExample VariableA symbol, usually a letter (like x or y), that represents an unknown numerical value.In the equation `7x - 4 = 3x + 8`, the symbol `x` is the variable. Like TermsTerms that have the same variable raised to the same power. Constant terms (plain numbers) are also like terms.In the expression `5y + 8 - 2y + 3`, the terms `5y` and `-2y` are like terms, and `8` and `3` are like terms. Inverse OperationsOperations that 'undo' each other. Addition and subtraction are inverse operations; multiplication and division are inverse operations.To undo adding 5 to a variable, you use the inverse operation: subtracting 5. Distributive PropertyA property that states that multiplying a sum by a number is the same as multiplying each addend by the number and then addi...

Subtraction Property of Equality If `a = b`, then `a - c = b - c` You can subtract the same value or term from both sides of an equation without changing the equation's solution. This is the primary tool for moving a variable term from one side to the other. Addition Property of Equality If `a = b`, then `a + c = b + c` You can add the same value or term to both sides of an equation without changing the equation's solution. This is used to move negative or subtracted terms across the equals sign. Division Property of Equality If `a = b` and `c ≠ 0`, then `a/c = b/c` You can divide both sides of an equation by the same non-zero number. This is the final step used to isolate the variable when it has a coefficient other than 1.