Question

Solve each equation. Check your solution. $$2(d+6)=3 d-1$$

   Solve each equation. Check your solution.
$$2(d+6)=3 d-1$$

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 8, Problem 12

Instant Answer

Solved by Expert Ashley Volpe

05/26/2020

Step 1

Step 1: First, distribute the 2 in the left side of the equation: \[2d + 12 = 3d - 1\] Show more…

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Solve each equation. Check your solution. $$2(d+6)=3 d-1$$

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Key Concepts

Linear Equations

Linear equations in one variable are algebraic expressions that involve a single variable and can be represented in the form ax + b = 0. They are foundational in algebra, and solving them involves finding the value of the variable that makes the equation true. This concept is critical as it forms the basis for understanding more complex equation solving techniques.

Distributive Property

The distributive property allows you to multiply a term by each term within a bracket, making it easier to simplify expressions and equations. It is a key algebraic strategy that helps in breaking down equations into simpler components by transforming expressions like a(b + c) into ab + ac.

Isolating Variables

Isolating the variable refers to manipulating an equation in order to get the unknown variable on one side by itself. This is a crucial step in solving equations, as it directly leads to determining the value of the variable through inverse operations such as addition, subtraction, multiplication, and division.

Checking Solutions

Checking solutions involves substituting the obtained solution back into the original equation to verify if it satisfies the equation. This process is important because it confirms the correctness of the solution and helps identify any potential mistakes in the solving process.

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