Solve equations involving like terms

Learning Objectives Identify like terms within a one-variable equation. Combine like terms on one side of an equation to simplify it. Apply inverse operations (addition/subtraction) to isolate the variable. Apply inverse operations (multiplication/division) to solve for the variable. Solve one-variable equations that require combining like terms. Check their solutions by substituting the value back into the original equation. Ever wonder how detectives solve mysteries? 🕵️‍♀️ In math, we're like detectives solving for a hidden number in an equation! In this lesson, you'll learn how to simplify equations by grouping similar parts, called 'like terms,' and then find the unknown value. This skill is super important for solving many kinds of math problems and...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, usually containing an equals sign (=).$$x + 5 = 12$$ VariableA letter or symbol (like x, y, or a) that represents an unknown number or value.In $$3x + 7 = 16$$, 'x' is the variable. TermA single number, a variable, or a product of numbers and variables. Terms are separated by addition or subtraction signs.In $$4x + 2y - 5$$, the terms are $$4x$$, $$2y$$, and $$5$$. Like TermsTerms that have the exact same variable(s) raised to the exact same power. Only the numerical coefficient can be different.$$3x$$ and $$5x$$ are like terms. $$4$$ and $$10$$ are also like terms (constants). CoefficientThe numerical factor (number) that multiplies a variable in a term.In $$7x$$, $$7$$ is the coefficie...

Combining Like Terms $$ax + bx = (a+b)x$$ or $$ax - bx = (a-b)x$$ To combine like terms, add or subtract their coefficients while keeping the variable part the same. This simplifies one side of an equation. Addition/Subtraction Property of Equality If $$a = b$$, then $$a + c = b + c$$ and $$a - c = b - c$$ You can add or subtract the same number from both sides of an equation without changing its balance or solution. This is used to isolate the variable term. Multiplication/Division Property of Equality If $$a = b$$ and $$c \neq 0$$, then $$ac = bc$$ and $$\frac{a}{c} = \frac{b}{c}$$ You can multiply or divide both sides of an equation by the same non-zero number without changing its balance or solution. This is used to solve for the variable after it's isolated...