Solving Multi-Step Equations Learning Objective(s) · Use properties of equality together to isolate variables and solve algebraic equations. · Use the properties of equality and the distributive property to solve equations containing parentheses, fractions, and/or decimals. Introduction There are some equations that you can solve in your head quickly. For example – what is the value of y in the equation 2y = 6? Chances are you didn’t need to get out a pencil and paper to calculate that y = 3. You only needed to do one thing to get the answer, divide 6 by 2. Other equations are more complicated. Solving without writing anything down is difficult! That’s because this equation contains not just a variable but also fractions and terms inside parentheses. This is a multi-step equation, one that takes several steps to solve. Although multi-step equations take more time and more operations, they can still be simplified and solved by applying basic algebraic rules. Using Properties of Equalities Remember that you can think of an equation as a balance scale, with the goal being to rewrite the equation so that it is easier to solve but still balanced. The addition property of equality and the multiplication property of equality explain how you can keep the scale, or the equation, balanced. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you’ll keep both sides of the equation equal. If the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division.
If the equation is not in the form, ax + b = c, you will need to perform some additional steps to get the equation in that form. In the example below, there are several sets of like terms. You must first combine all like terms.
Some equations may have the variable on both sides of the equal sign. We need to “move” one of the variable terms in order to solve the equation.
Here are some steps to follow when you solve multi-step equations.
The examples below illustrate this sequence of steps.
Advanced Question Identify the step that will not lead to a correct solution to the problem. A) Multiply both sides of the equation by 2. B) Add to both sides of the equation. C) Add to the left side, and add to the right side. D) Rewrite as . Solving Equations Involving Parentheses, Fractions, and Decimals More complex multi-step equations may involve additional symbols such as parentheses. The steps above can still be used. If there are parentheses, you use the distributive property of multiplication as part of Step 1 to simplify the expression. Then you solve as before.
What this means is that when a number multiplies an expression inside parentheses, you can distribute the multiplication to each term of the expression individually. Then, you can follow the routine steps described above to isolate the variable to solve the equation.
In which of the following equations is the distributive property properly applied to the equation 2(y +3) = 7? A) y + 6 = 7 B) 2y + 6 = 14 C) 2y + 6 = 7 D) 2y + 3 = 7 If you prefer not working with fractions, you can use the multiplication property of equality to multiply both sides of the equation by a common denominator of all of the fractions in the equation. See the example below.
Of course, if you like to work with fractions, you can just apply your knowledge of operations with fractions and solve.
To clear the fractions from , we can multiply both sides of the equation by which of the following numbers? 3 6 9 27 A) 9 B) 9 or 27 C) 6 D) 3 or 9 Regardless of which method you use to solve equations containing variables, you will get the same answer. You can choose the method you find easier! Remember to check your answer by substituting your solution into the original equation. Just as you can clear fractions from an equation, you can clear decimals from the equation in the same way. Find a common denominator and use the multiplication property of equality to multiply both sides of the equation.
Advanced Question Solve for a: A) a = 2 B) a = 1 C) a = 0 D) a = -2 Summary Complex, multi-step equations often require multi-step solutions. Before you can begin to isolate a variable, you may need to simplify the equation first. This may mean using the distributive property to remove parentheses, or multiplying both sides of an equation by a common denominator to get rid of fractions. Sometimes it requires both techniques. What is a 2 step equation example?Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are: 2x + 3 = 7.
What is multiA multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations. So get your mathematical toolbox out!
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