Question

Solve each equation and check. $$ 5 y-3=11+3 y $$

   Solve each equation and check.
$$
5 y-3=11+3 y
$$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 2, Problem 8

Instant Answer

Solved by Expert Xiaomeng Zhang

07/15/2020

Step 1

This gives us: $$5y - 3y = 11 + 3y - 3y$$ which simplifies to: $$2y - 3 = 11$$ Show more…

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Solve each equation and check. $$ 5 y-3=11+3 y $$

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Key Concepts

Linear Equations

Linear equations are equations of the first degree, meaning that the variable is raised to the power of one. They are characterized by their straightforward structure, which allows them to be solved using basic algebraic operations. Mastery of linear equations is fundamental to algebra as they model many practical situations, and their methods carry over to more complex equations.

Isolating the Variable

Isolating the variable involves rearranging the equation so that the unknown variable stands alone on one side of the equation. This process typically includes adding, subtracting, multiplying, or dividing both sides of the equation by the same value to preserve equality. It is a critical step in solving equations and understanding the structure of the solution.

Inverse Operations

Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division. In solving equations, inverse operations are used to eliminate constants or coefficients attached to the variable, making it easier to isolate and solve for the unknown value. This concept is essential in reducing equations to a simpler form.

Verification of Solutions

Verification of solutions involves substituting the obtained value back into the original equation to ensure that it satisfies the equality. This step is important as it checks the correctness of the solution and helps in identifying any errors made during the manipulation of the equation. It reinforces understanding of equation balance and the consistency of the solution.

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