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Solve two-step linear equations

Understanding centers on equations in one variable of the form ax+b=cax+b=c or x/a+b=cx/a+b=c, where numerical coefficients and constants may include integers, decimals, or simple fractions. The learner reasons that inverse operations, applied in reverse order to both sides, preserve equality and isolate the variable, and verifies solutions by substitution; this establishes foundations for formulas, functions, and modeling. Equations with variables on both sides, parentheses requiring multiple distributive steps, or more abstract cases are outside this scope.

Detailed Explanation: Solve two-step linear equations

To solve a two-step linear equation, undo the operations in the reverse order of how they were applied to the variable. Whatever you do to one side, do to the other side to keep the equation balanced.

Solve:

3x+5=203x+5=20
  1. Undo the addition of 55. Subtract 55 from both sides:
3x+5−5=20−53x+5-5=20-5 3x=153x=15
  1. Undo the multiplication by 33. Divide both sides by 33:
3x3=153\frac{3x}{3}=\frac{15}{3} x=5x=5
  1. Check the solution by substituting 55 for xx in the original equation:
3(5)+5=15+5=203(5)+5=15+5=20

The statement is true, so the solution is:

x=5\boxed{x=5}

Learn by doing: Solve two-step linear equations

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Two-Step Equation - Subtraction and Division - Solve


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