Question

Solve the given linear equation. $$2 x+3=5-2 x$$

   Solve the given linear equation.
$$2 x+3=5-2 x$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 0, Problem 22

Instant Answer

Solved by Expert Ankit Gupta

07/24/2020

Step 1

To do this, we add $2x$ to both sides of the equation to cancel out the $-2x$ on the right side. This gives us: $$2x + 2x + 3 = 5 - 2x + 2x$$ Show more…

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Solve the given linear equation. $$2 x+3=5-2 x$$

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Key Concepts

Isolation of the Variable

Isolation of the variable is the process of rearranging an equation so that the unknown variable is on one side of the equation and all constants on the other. This technique is a central method used to solve equations and find the value of the variable that satisfies the equation.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting coefficients of terms that have the same variable raised to the same power. This process simplifies the equation and is crucial for making the variable isolation process more straightforward.

Properties of Equality

The properties of equality, including the addition, subtraction, multiplication, and division properties, allow for the manipulation of equations while maintaining equality. They are essential tools that ensure the balance of an equation is preserved when isolating the variable.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Such equations graph as straight lines and have a constant rate of change, making them fundamental in algebra for modeling relationships with a constant slope.

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