Solving Two-Step Equations Tutorial 6b

Solving Two-Step Equations A two-step equation is an equation that has two operations. The following equations are one-step equations: y + 2 = 12 or 5x = 40 or a/4 = 10. These are two-step equations: 2x + 5 = 11 or 12r – 7 = 17 or y/8 + 6 = 10

Solving Two-Step Equations One way to solve an equation is to get the variable alone on one side of the equal sign. You can do this by using inverse operations, which are operations that undo one another.

Solving Two-Step Equations Addition and subtraction are inverse operations. You can use subtraction to undo addition and addition to undo subtraction . Multiplication and division are inverse operations. You can use division to undo multiplication and multiplication to undo division.

Example #1 Think to yourself: What is being done to the variable (x)? Suppose you earn $4 per hour baby-sitting and pay $1 in bus fare each way. You want to buy a T-shirt that costs $10. To find the number of hours you must work to buy the T-shirt, solve the equation 4x – 2 = 10. Think to yourself: What is being done to the variable (x)? A 4 is being multiplied to the variable (x). And a 2 is being subtracted from the term having the variable (x). Division undoes multiplication and -- Addition undoes subtraction. This is a two-step equation because there are two operations that must be undone.

Example #1 Suppose you earn $4 per hour baby-sitting and pay $1 in bus fare each way. You want to buy a T-shirt that costs $10. To find the number of hours you must work to buy the T-shirt, solve the equation 4x – 2 = 10. When solving a two-step equation - - always undo any addition or subtraction first! Then undo any multiplication or division. Remember, whatever you do to one side of an equation you must also do to the other side.

Example #1 Suppose you earn $4 per hour baby-sitting and pay $1 in bus fare each way. You want to buy a T-shirt that costs $10. To find the number of hours you must work to buy the T-shirt, solve the equation 4x – 2 = 10. To undo the subtraction, add a 2 to each side of the equation. 4x – 2 = 10 + 2 + 2 To undo the multiplication, divide by 4 on each side of the equation. 1 3 4x = 12 4 4 1 1 x is now all alone on one side of the equation! x = 3 Always check your answers! 4x - 2 = 10; Does x =3? 4•3 - 2 = 10 is true! You will have to work for 3 hours in order to buy the T-shirt.

Example #2 Solve the Equation: - 5 - 5 (-12)• •(-12) - 4 = 48 = m 1 1 To undo the addition, subtract a 5 from each side of the equation. - 5 - 5 To undo the division, multiply by -12 on each side of the equation. 1 (-12)• •(-12) - 4 = 1 48 = m x is now all alone on one side of the equation! Always check your answers!

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