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Master Two-Step Linear Equations: Solve ax + b = c Easily

Understanding ratios and unit rates

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Square and cube roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Proportions

Solving two-step linear equations: ax + b = c, x/a + b = c

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Proportional vs. non-proportional

Understanding tables of values of linear relationships

Linear relation

Identifying proportional relationships

Scale drawings and similar figures

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Classifying real numbers

Understanding the number systems

Rational vs. Irrational numbers

Prime and composite numbers

Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Determining common factors

Common Factors — Word problem: bouquet

Common Factors — Word problem: party

Common Factors

Factors

Determining common multiples

Common Multiples — Word problem: meals

Common Multiples — Word problem: watches

Multiples

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

GCF and LCM

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Integer exponents

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Using exponents to describe numbers

Expanded powers

Multiplying decimals by powers of 10

Multiplying decimals by powers of 10 — Find the decimal number

Multiplying decimals by powers of 10 — Find the power of 10

Multiplying decimals by powers of 10 — Moving the decimal

Multiplying decimals by powers of 10 — Word problem: factory

Exponents — Powers of 10

Dividing decimals by power of 10

Dividing decimals by powers of 10 — Word problem

Dividing decimals by powers of 10 — Word problem: backwards

Dividing decimals by powers of 10 — Find the power of 10

Dividing decimals by powers of 10 — Moving the decimal

Dividing decimals by powers of 10 — Find the exponent

Assignments

Challenge Zone

Foundation Review

ALEKS Ratios and Proportions

Ratios and Proportional Reasoning

Real Numbers and Number Theory

sample

math

Intro

Word problem: Finding John's exercise hours using a two-step equation

Solving a two-step equation with mixed fractions

Solving a two-step equation with decimals and a fraction

- Hi, welcome to this question right here. Wow, this is the type of question where you don't just cross multiply right away. You have to remove something else before you can do the short cut. What happened is we've got a four over five plus five over 4x equals one over three. Now the idea is simple. You want to solve the x which is here. You have to remove anything that is furthest away from there first. The four over five has to go first. What we'll do is, we'll keep the five over 4x as it is. We're going to subtract the four over five from both sides. We're going to subtract the four over five from this side and from this side. Now it is still mathematically the same thing. If you subtract the four over five from here, that four over five is gone from the question. Then it's just one over three minus the four over five. What I'm going to recommend if you're going to show all your work then you will have to combine these two fractions together. Now when it comes to fractions, adding and subtracting, you have to keep the denominator the same. That's a three and that's a five so it doesn't work. You have to find the lowest common denominator between the three and the five. The lowest common denominator between the three and the five would be the 15. If you want to change the three to 15 you have to times it by five. You do the same to the bottom, you have to do the same to the top. Three times five is 15, and one times five is still the five. This one over here because you want to get to 15, right? 
Mathematically, you'll be thinking five times what gives me 15? Times three. If you times the three to the bottom then you will have to times it by three to the top as well. Three times four is 12. Let's write down the work in a different color so you can see what happened there. What happened here is we times this by a five, we times that by a five, we times that by a three, and we times that by a three. Right now, we've got a five minus 12 all over 15. If you want, I would recommend that you actually do it this way. Change the common denominator into one denominator. You can do that. Then the top is just five minus 12. So you won't do anything weird. You'll just keep the denominator the same but this time you'll just go five minus the 12 on the top, I think it's negative seven if I remember correctly. Yes, and that's negative seven over 15 so far. On the left hand side, the five over 4x is still waiting for you. I would recommend you write the x right beside the five. It makes it look a little bit nicer. We're trying to solve the x still. But this time if you look at your question now. It's five x over four equal to the negative seven over 15. Two fractions on either side of the equals sign. What can you do? 
Cross multiply. I will actually now take the cross multiply method. I will take the four and multiply it to the negative seven. Take the five and multiply it down to the 15. Why do I do that? I want to keep the x by itself on the top. Now the x is on the top by itself, it's alone but that's what we want. Take the four times the negative seven, it's negative 28. Take the five times the 15, that's too big for me, it's 75. Then we've got 28 over 75. Is is possible we can reduce this number? Let me get a quick calculation here. Nothing we can do. Final answer. Negative 28 over 75. Thanks for watching.

Solving a fraction equation with subtraction before cross-multiplying

Solving x/(-2.14) + 0.86 = 6.32 with decimal arithmetic

Solving 2/3 minus x/2 equals 4/7 using fraction operations

Solving a two-step equation with decimals: 3.07 = 0.3x - 4.6

Solving a two-step equation with fractions using common denominators

Solving x/a + b = c with decimals using cross multiplication

Solving a two-step equation with mixed fractions and variable V

Modeling word problems as quadratic functions for revenue and area

Solving two-step linear equations literally means solving the equations in two major steps. First, we need to isolate the unknown "x" to one side of the equation. You can then solve the "x". To complete these two steps, you may need to perform addition, subtraction, division, multiplication, cross multiplication, and so on. When the equation has fractions, you may also need to find the common denominator before proceeding further. Seems complicated? No worries! You will learn all the tricks in this section.

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step Linear equations: ax+b = c, x/a +b = c

How to solve two-step linear equations

Model and solve one-step linear equations: ax = b, x/a = b

Solving two-step linear equations using addition and subtraction: ax + b = c

Solving two-step linear equations using multiplication and division: x/a + b = c

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Overview

Mastering Two-Step Linear Equations: Your Guide to Solving ax + b = c

What You'll Learn

Isolate variables in two-step equations using inverse operations

Apply addition, subtraction, multiplication, and division to solve for x

Solve equations with fractions by finding common denominators

Use cross-multiplication when equations involve fractions on both sides

Verify solutions by substituting back into the original equation

What You'll Practice

Solving equations of the form ax + b = c with integers and decimals

Working with fractional equations requiring common denominators

Cross-multiplying to solve equations with variables in denominators

Applying two-step solving to word problems involving revenue and area

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

12 Video lessons

Practice exercises

Learning resources

Skills

Two-Step Equations

Inverse Operations

Fractions

Cross-Multiplication

Common Denominators

Algebraic Manipulation

Word Problems