Solving One Step Equation with Division in the Equation

Solving one step equations can be a very simple process! This is the beginning to solving much more complex mathematical problems. Before we can go into solving these equations there are a few terms you need to know.  VARIABLE- a “mystery” number that is represented by a letter from the alphabet. This letter in Algebra is usually an x. Do not confuse the variable x with the multiplication symbol. Multiplication in Algebra is usually represented with a •. For example 2•2=4. A number standing next to a variable represents multiplication in Algebra. For example 2x means 2 times x.  COEFFICENT- The number standing next to the variable. For example the coefficient of 2x is 2 because the 2 is standing right next to the variable.  EQUATION- Any mathematical statement that contains an equal sign. For example 2x = 2 is an equation because there is an equal sign, but 4x is not because there is no equal sign.  INVERSE- literally means the opposite. The inverse of addition is subtraction and the inverse of subtraction is addition. Furthermore the inverse of multiplication is division and the inverse of division is multiplication. So now that we have the basic terms down we need to go step by step in solving one step equations. We will take an example from each type.

Solving One Step Equation with Addition in the Equation X + 4 = 12  Step one: Determine whether the mathematical sentence is an equation. If it has an equal sign you can solve, if it does not you cannot solve. This mathematical sentence is an equation therefore you can move to the next step.  Step two: Determine what type of math is in the sentence. Is it addition, subtraction, multiplication, or division? In the equation above addition is being performed.  Step 3: Take the inverse of addition (since it is the one being used in the example equation) with the number used. REMEMBER: what you do to one side of the equation you must do to the other side!

X + 4 = 12 -4 -4  4 -4 is zero so that will cross out the fours in this equation (you really want that!) which leaves you with: X = 12 -4  Step 4: Finish the computation! Since you subtracted 4 on one side of the equation, you must subtract 4 from the other side of the equation. So 12 -4 = 8.  So the answer to x + 4 = 12 is x = 8!

Solving One Step Equation with Subtraction in the Equation X - 4 = 12  Step one: Determine whether the mathematical sentence is an equation. If it has an equal sign you can solve, if it does not you cannot solve. This mathematical sentence is an equation therefore you can move to the next step.  Step two: Determine what type of math is in the sentence. Is it addition, subtraction, multiplication, or division? In the equation above subtraction is being performed.  Step 3: We need to move everything so that the variable is by itself on one side of the equation. Take the inverse of subtraction (since it is the one being used in the example equation) with the number used. REMEMBER: what you do to one side of the equation you must do to the other side! X - 4 = 12 +4 +4  4 -4 is zero so that will cross out the fours in this equation (you really want that!) which leaves you with:

X = 12 +4  Step 4: Finish the computation! Since you added 4 on one side of the equation, you must add 4 from the other side of the equation. So 12 + 4 = 16.  So the answer to x - 4 = 12 is x = 16!

Solving One Step Equation with Multiplication in the Equation 4x = 12  Step one: Determine whether the mathematical sentence is an equation. If it has an equal sign you can solve, if it does not you cannot solve. This mathematical sentence is an equation therefore you can move to the next step.  Step two: Determine what type of math is in the sentence. Is it addition, subtraction, multiplication, or division? In the equation above Multiplication is being performed. Remember that if a number and a letter are standing next to each other then it is representing multiplication  Step 3: We need to move everything so that the variable is by itself on one side of the equation. Take the inverse of multiplication (since it is the one being used in the example equation) with the number used. REMEMBER: what you do to one side of the equation you must do to the other side! 4x = 12 4 4  4 divided by 4 is 1 so that will cause the 4 to vanish. (Because your new coefficient is 1 and anything times 1 is itself (you really want that!) which leaves you with:

X = 12 4  Step 4: Remember that when you see fractions in algebra that really denotes division. So you need to figure out 12 divided by 4.  So the answer to 4x = 12 is x = 3!

Solving One Step Equation with Division in the Equation x=3 4  Step one: Determine whether the mathematical sentence is an equation. If it has an equal sign you can solve, if it does not you cannot solve. This mathematical sentence is an equation therefore you can move to the next step.  Step two: Determine what type of math is in the sentence. Is it addition, subtraction, multiplication, or division? In the equation above division is being performed. Remember that if a number looks like a fraction then it denotes division!  Step 3: We need to move everything so that the variable is by itself on one side of the equation. Take the inverse of multiplication (since it is the one being used in the example equation) with the number used. REMEMBER: what you do to one side of the equation you must do to the other side! 4•x=3•4 4  4 divided by 4 is 1 so that will cause the 4 to vanish. (Because your new coefficient is 1 and anything times 1 is itself (you really want that!) which leaves you with:

X=3•4  Step 4: Remember that a dot denotes multiplication  So the answer is x = 12!

 Two step equations are just like one step equations, just with an extra step. 2x – 4 = 8  Step one: Determine if the sentence is an equation. Yes it is an equation.  Step two: Start with the number furthest away from the variable and take the inverse. Remember what you do to one side of the equation you do to the other side as well!  2x – 4 = 8 + 4 +4 --------------------------- Step 3: When you take the inverse of that number you should zero out those numbers on the side of the equation. In this example 4 – 4 = 0 which will leave nothing on that side of the equation, but since what you do to one side you must do to the other, you must add 4 to 8 which gives you 12. Your new equation looks like this: 2x = 12  Step 4: Now you have gone down to a one step equation and can follow the rules to one step equations. 2x = 12 2 2  Step 5: Follow the rules to one step equations as shown above. Since your coefficient is 2 you must divide by 2 on both sides of the equation. The twos on the left side of this equation will cancel each other out which will leave you with x. 12 divided by 2 is 6. 2x – 4 = 8 and your answer will be x = 6