We can apply the same techniques we used for solving a one-step equation which contained absolute value to an equation that will take more than one step to solve. Learn the 4 steps for helping students master these tricky tasks! For example, suppose somebody asked you to find the set of all senior citizens who are less than five years old. It does not matter which term gets moved, $4x$ or $2x$; however, to avoid negative coefficients, you can move the smaller term. ( Log Out /  Solve for w. $3\left|4w–1\right|–5=10$. Multi step equations are solved by applying similar techniques used in solving one-step and two-step equations. In the two videos that follow, we show examples of how to solve an absolute value equation that requires you to isolate the absolute value first using mathematical operations. Fluid Notes application will be downloaded on the devices before the class. For example, the set of months with 32 days. Examples 2. Discuss and ask them why they gave answer of one. However, most inequalities require several steps to arrive at the solution. Multi-step income statement is one of the two most commonly used income statement formats. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Then they need to collect like terms and solve the equation using Properties of Equality. A poster about three different solutions for equations. ( Log Out /  A multi-step equation sometimes involves combining like terms. That is because this equation contains not just a variable but also fractions and terms inside parentheses. $\displaystyle \begin{array}{r}3y+2\,\,\,=\,\,11\\\underline{\,\,\,\,\,\,\,-2\,\,\,\,\,\,\,\,-2}\\3y\,\,\,\,=\,\,\,\,\,9\end{array}$. $\begin{array}{r}4x-6=10\\\underline{\,\,\,\,+6\,\,\,+6}\\2x=16\end{array}$. Consider the equation 2(x + 1) – x = 5. Students will be given the chance to work together, students who have learning difficulties could get help from their peers during group section. Explain the students that some equations contain expressions with grouping symbols that need to get expanded by using Distributive Property. We can apply the same techniques we used for solving a one-step equation which contained absolute value to an equation that will take more than one step to solve. Change ), Technology in Classroom Final Portfolio Project, Assistive Devices and Technology in Education of Children, Development of Authentic Assessments for The Middle School Classroom, Lessons Learned from the Teacher Education Program to Classroom, Revised Lesson Plan on Solving Multi-step Equations. Here’s an example. Other equations are more complicated. To solve a multi-step equation, we would start by trying to simplify the equation by combining like terms and using the distributive property whenever possible. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you will keep both sides of the equation equal. Begin the class with bell ringer on the SMARTboard which includes following three questions that will remind the previous lesson: Include the activities and the content that you will teach (lecture notes can be separate). They will begin with an example such as: Ask students how many solutions that equation could have. 2x = 20 x = 10 4x + 2 = 4x + 2 2 = 2 One Solution Since 2 = 2 is true, then there are infinitely many solutions that make this equation true. Choose the variable term to move—to avoid negative terms choose $2x$, $\,\,\,4x-6=2x+10\\\underline{-2x\,\,\,\,\,\,\,\,\,\,-2x}\\\,\,\,4x-6=10$. Make them put the chart in their notebooks. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. After few answers explain group multiplication. Materials, Technology, Adaptations, Differentiation Strategies. Multi-step word problems require a special set of problem-solving strategies. Solving Multi-Step Equations The word “multi” means more than two, or many. $\displaystyle \begin{array}{r}4w-1=5\,\,\,\,\,\,\,\,\,\,\,\,\text{or}\,\,\,\,\,\,\,\,\,\,4w-1=-5\\\underline{\,\,\,\,\,\,\,+1\,\,+1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{\,\,\,\,\,\,\,\,\,+1\,\,\,\,\,+1}\\\,\,\,\,\,\underline{4w}=\underline{6}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{4w}\,\,\,\,\,\,\,=\underline{-4}\\4\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\\\,\,\,\,\,\,\,\,w=\dfrac{3}{2}\normalsize \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,w=-1\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,w=\dfrac{3}{2}\normalsize \,\,\,\,\,\text{or}\,\,\,\,\,-1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{array}$, $\displaystyle \begin{array}{r}\,\,\,\,\,3\left| 4w-1\, \right|-5=10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\left| 4w-1\, \right|-5=10\\\\3\left| 4\left(\dfrac{3}{2}\normalsize\right)-1\, \right|-5=10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\left| 4w-1\, \right|-5=10\\\\\,\,\,\,\,\,3\left|\dfrac{12}{2}\normalsize -1\, \right|-5=10\,\,\,\,\,\,\,3\left| 4(-1)-1\, \right|-5=10\\\\\,\,\,\,\,\,\,\,3\left| 6-1\, \right|-5=10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\left| -4-1\, \right|-5=10\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\left(5\right)-5=10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\left| -5 \right|-5=10\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,15-5=10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,15-5=10\\10=10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10=10\end{array}$. In the next example, you will see that there are parentheses on both sides of the equal sign, so you will need to use the distributive property twice. You only needed to do one thing to get the answer: divide $6$ by $2$. In the equation $2x-3^2=10x$, the variable is $x$, a coefficient is $10$, a term is $10x$, an expression is $2x-3^2$. Show the part of the presentation which include a chart of three different types of equations. Then we can proceed as we did in the previous example. $\begin{array}{r}3\left|4w-1\right|-5=10\\\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,+5\,\,\,+5}\\ 3\left|4w-1\right|=15\end{array}$. Just like we saw in one-step and two-step equations, the main objective of solving multi step equations is also to isolate the unknown variable on either the RHS or LHS of the equation while keeping a constant term on the opposite side. As with solving equations, we must use the order of operations to find the correct solution. Visual and audio learners will be supported with a presentation and lecture. Name Goksel Marmara                                                                               Date 10/03/2014, Course 8th Grade Mathematics                                                          Period(s)   5th Period, Common Core and/or Illinois Learning Standards, Solve each equations. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Write the two equations that will give an absolute value of 5 and solve them. Change ), You are commenting using your Twitter account. Change ), You are commenting using your Google account. Give them 5 minutes to solve following equations. Multi-step income statement involves more than one subtraction to arrive at net income and presents more information. Solve each equation for p by isolating the variable. Now the absolute value is isolated. To solve this equation, we need to “move” one of the variable terms. $4$ and $7$ are also like terms and can be added. Change ), You are commenting using your Facebook account. The set of squares with 5 sides. In this video, we show an example of solving equations that have variables on both sides of the equal sign. Therefore, your set contains no elements and is the null set. We call a set with no elements the null or empty set. EE.7 Solve linear equations in one variable. Some equations may have the variable on both sides of the equal sign, as in this equation: $4x-6=2x+10$. IPad will be used for the group work. See answer Stargazingstudent is waiting for your help. Show three different equations on the SMARTboard and let them discuss: Group students for the next task and give the following information: Ask students if they understand the groups of equations. Write and solve equations with grouping symbols. An equation that is true for every value of the variable is called an identity. Homework essay which includes multi step equations to encourage what have been learned. $\begin{array}{c}\dfrac{2x}{2}\normalsize=\dfrac{16}{2}\\\\\normalsize{x=8}\end{array}$. Value). After solving the equations give a brief information about solutions that these equations have. Another example of the null set is the set of all even numbe…