Lesson 2.2a EQ: How do I solve a literal equation for a specified variable? Standard(CED.4) Equations

Introduction Concept: Literal Equations EQ: How do I solve a literal equation for a specified variable? (Standard: CED.4) Vocabulary: Literal Equation

Review Last class we went more in depth with the proofs of an equation Today, we will dive into what a literal equation is.

What is a Literal Equation? Literal equations are equations that involve two or more variables. Sometimes it is useful to rearrange or solve literal equations for a specific variable in order to find a solution to a given problem. In this lesson, literal equations and formulas, or literal equations that state specific rules or relationships among quantities, will be examined.

Steps: Solving a Literal Equation Isolate the variable you’re solving by moving all other terms to the opposite side of the equal sign. Combine like terms on each side of the equal sign. Solve for the variable. Simplify.

Example 1: Solve for x 3x=𝑦 3x = y Steps 1. x = 𝑦 3 1. Isolate the variable you’re solving for by moving all other terms to the opposite side of the equal sign. 2. N/A 2. Combine like terms on each side of the equal sign. 3. N/A 3. Solve for the variable. 4. N/A 4. Simplify.

Example 2: Solve for x y= 𝑥 5 +4 𝐲= 𝒙 𝟓 +𝟒 Steps 1. 𝑦−4= 𝑥 5 1. Isolate the variable you’re solving for by moving all other terms to the opposite side of the equal sign. 2. 𝑦−4= 𝑥 5 2. Combine like terms on each side of the equal sign. 3. 5 𝑦−4 = 𝑥 5 ∙5 3. Solve for the variable. 4. 5𝑦−20=𝑥 4. Simplify

Example 3: Solve for x 2x - 4y = 7 Steps 1. 2x = 7+ 4y 1. Isolate the variable you’re solving for by moving all other terms to the opposite side of the equal sign. 2. 2x = 7 + 4y 2. Combine like terms on each side of the equal sign. 3. 2𝑥 2 = 7+4𝑦 2 3. Solve for the variable. 4. x= 7 2 +2𝑦 4. Simplify.

Example 4: Solve for y 4x – 2y = 12 Steps 1. 4x – 2y = 12 1. Isolate the variable you’re solving for by moving all other terms to the opposite side of the equal sign. 2. -2y = 12 – 4x 2. Combine like terms on each side of the equal sign. 3. −2𝑦 −2 = 12−4𝑥 −2 3. Solve for the variable. 4. y = -6 + 2x 4. Simplify.

Example 5: Solve for y 𝑥−7= 𝑦 3 𝒙−𝟕= 𝒚 𝟑 Steps 1. 3 𝑥−7 = 𝑦 3 ∙3 1. Isolate the variable you’re solving for by moving all other terms to the opposite side of the equal sign. 2. 3 𝑥−7 = 𝑦 3 ∙3 2. Combine like terms on each side of the equal sign. 3. 3 𝑥−7 =𝑦 3. Solve for the variable. 4. 3𝑥−21=𝑦 4. Simplify.

You Try: Solve for y 15x – 5y = 25

You Try: Solve for y 4y + 3x = 16

You Try: Solve for y 𝑦 8 +24= 𝑥