1.2 Commutative and Associative Properties
1.3 Identity and Inverse Properties
2.3 Fractions Equal to Whole Numbers
2.4 Converting Mixed and Improper Fractions
2.5 Adding and Subtracting Fractions with Like Denominators
2.6 Adding and Subtracting Fractions with Unlike Denominators
2.9 Understanding Keep, Change, Flip
3.1 Converting Fractions to Decimals
3.2 Converting Decimals to Fractions
3.3 Converting Integers to Decimals and Fractions
3.7 Understanding Proportional Ratios
3.8 Identifying Proportional Ratios
3.9 Comparing Ratios with Rates and Prices
3.11 Converting Percent to Fraction and Decimal
4.1 Operations and Expressions
4.3 Expressions with Addition and Subtraction
4.4 Expressions with Multiplication and Division
4.5 Expressions with Exponents
4.6 Expressions with Decimals and Fractions
4.10 Understanding Distributive Property
4.11 Using the Distributive Property
4.12 Combining Like Terms with Distributive Property
5.2 The Goal of Solving Equations
5.3 Checking the Answer to an Equation
5.4 Solving Equations with Addition and Subtraction
5.5 Solving Equations with Multiplication
5.6 Solving Equations with Division
5.7 Starting a Two-Step Equation
5.8 Solving Two-Step Equations
5.9 Simplifying and Solving Two-Step Equations
5.11 Translating Math Expressions
5.12 Translating Math Equations
5.13 Strategies for Algebraic Word Problems
6.2 Comparing Integers and Decimals
6.4 Graphing Inequalities on Number Lines
6.5 Writing Inequalities from Number Lines
6.6 Translating Inequalities from Word Problems
6.7 Solving Inequalities with Addition and Subtraction
6.8 Solving Inequalities with Multiplication and Division
6.9 Inequalities with Negative Numbers
6.10 Solving Inequalities with Negative Numbers
6.11 One-Step Inequality Word Problems
6.12 Writing Inequalities Different Ways
6.13 Solving Two-Step Inequalities
Math Basics > Unit 5 Equations > Lesson 5.7 Starting a Two-Step Equation
Click play to watch the video and answer the questions for points!
For each equation, click on the number that we need to "undo" first.
In our last lesson, we looked at solving one-step equations, meaning there was only one number that we needed to undo to get our variable isolated. Now we're going to look at solving two-step equations. So the challenge is when there's two numbers that we need to undo, where do we begin? Here is an example. We have two x minus eight equals 34. I'm going to draw a line through the equal sign so we can see the left and right sides of the equation clearly. And we can see our variable. X is on the left side. We have the two that's being multiplied by the x. Then we have the eight that's being subtracted. Well, that's two numbers that we need to undo to get x by itself. Which number do we undo first? To figure this out, we're going to revisit our old friend PEMDAS, the order of operations. Except instead of following the order of operations from beginning to end like we normally do, we're actually going to follow the order of operations in reverse. Think of solving equations as an undoing process. We have to do everything backwards to get down to x. So that means that we'll start by undoing addition and subtraction first, then work our way up to multiplication and division, and then exponents and then parentheses if we have those. Well, in this equation, we have the two that's being multiplied. So we have multiplication and then we have subtraction. Because the eight is being subtracted, this means that we would start by undoing the subtraction first that's at the bottom of our order of operations. So since eight is subtracted, we would undo the eight first. With this one, we have x over seven. Now remember, fraction represents division. So we can say this is x divided by seven. Then we have plus three equals five. I can see that x is on the left side of the equation again. And I have two numbers that I need to undo to get x by itself. I have the seven and the three. Which one do we undo first? We follow our order of operations, but in reverse. So the seven is being divided. We have x divided by seven. So that will get done during the division step. And then we have addition as we see plus three. Since the three goes along with addition and we undo addition and subtraction first, that means that we would start there when we want to isolate x. And then once the three is undone, we would move on to the seven. We're going to go on to our next lesson to figure out exactly how to finish solving these equations.
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