 # Foundations of Algebra

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Foundations of Algebra
Solving Two-Step Equations Foundations of Algebra

What is a Two-Step Equation?
An equation written in the form Ax + B = C , where two different algebraic operations are being performed on the variable.

Examples of Two-Step Equations
y/4 + 3 = 12 5n + 4 = 6 n/2 – 6 = 4

Steps for Solving Two-Step Equations
Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation. Steps for Solving Two-Step Equations

Opposite Operations Addition  Subtraction Multiplication  Division

Helpful Hints? Identify what operations are on the variable side. (Add, Sub, Mult, Div) “Undo” the operation by using opposite operations. Whatever you do to one side, you must do to the other side to keep equation balanced.

To solve two-step equations, undo the operations by working backwards.
Recall the order of operations as you answer these questions. 1) Ask yourself, What is the first thing we are doing to x? What is the second thing? To undo these steps, do the opposite operations in opposite order.

Solve the equations by doing the opposite operations in the opposite order.
Add 3 to both sides Simplify Clear the fraction -Multiply both sides by 2 Check your answer

2) Solve 2x - 1 = -3 Add 1 to both sides Simplify

3) Solve Add 4 to both sides Simplify

4) Solve 3y – 1 = 8 y = 3 y = -3 y =

5) Solve Clear the fraction - Multiply both sides by 2 Simplify

6) Solve d = -7 d = -19 d = -17 d = 17

7) Solve Subtract 3 from both sides Simplify
Clear the fraction – Multiply both sides by -7 Check your answer This one is tricky! Remember to always use the sign in front of the number.

8) Solve 5z + 16 = 51 z = -35 z = -7 z = 35 z = 7

9) Solve Subtract 1 from both sides Simplify
Clear the fraction - Multiply both sides by 5 Divide both sides by 3 Check your answer

2x – 5 = 17 3y + 7 = 25 5n – 2 = 38 12b + 4 = 28 Try These Examples

x = 11 y = 6 n = 8 b = 2 Check your answers!!!