Variables on Both Sides and Distributive Equations

Objective: Solve a linear equation with variables on both sides.

Prerequisite skills: distributive property and solving simple linear equations. Subtract the same variable term from each side to collect all variable terms on one side. Collect constants on the other side. If the remaining coefficient is nonzero, divide to isolate the variable. Common error: adding coefficients when moving a variable term. Restrictions and interpretation: Combine only like terms; distribute negative factors to every term.

Objective: Solve an equation containing a grouped expression and variables on both sides.

Distribute before combining like terms. Parentheses are not decorative: the factor outside multiplies every summand inside. After expansion, collect variables and constants using equivalent operations. Common error: multiplying the variable term but not the constant. Restrictions and interpretation: Combine only like terms; distribute negative factors to every term.

Objective: Handle a subtracted expression on both sides of an equation.

Subtracting a parenthesized expression is the same as multiplying it by −1. Expand each side independently before collecting variables; otherwise nested sign changes are easy to miss. Common error: keeping the inside minus after multiplying by a negative. Restrictions and interpretation: Combine only like terms; distribute negative factors to every term. Desmos and method choice: Use Desmos for arithmetic or a graph/table check when that reduces work. Enter parentheses explicitly and verify the requested quantity and units. Use the algebraic steps shown here for an exact result; a rounded graph display is not proof of exact equality.