Question

Solve for the indicated variable. $$ 2-(4 x+1)=3-(2 x-1) $$

   Solve for the indicated variable.
$$
2-(4 x+1)=3-(2 x-1)
$$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 29

Instant Answer

Solved by Expert Amy Jiang

06/30/2020

Step 1

$$ 2 - 4x - 1 = 3 - 2x + 1 $$ Show more…

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Solve for the indicated variable. $$ 2-(4 x+1)=3-(2 x-1) $$

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Key Concepts

Properties of Equality

The properties of equality are fundamental rules in algebra that allow us to perform the same operation on both sides of an equation without changing the equality. These properties ensure that the structure of the equation remains balanced and are crucial when adding, subtracting, multiplying, or dividing terms to solve an equation.

Isolating Variables

Isolating the variable means rearranging the equation so that the unknown variable stands alone on one side of the equation. This process often requires performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation, to progressively simplify and solve for the variable.

Linear Equations

Linear equations are mathematical statements of equality involving linear expressions, typically involving one or more unknown variables. They are of the first degree, meaning the highest power of the variable is one. The primary goal when solving a linear equation is to isolate the variable on one side to determine its value.

Combining Like Terms

Combining like terms involves simplifying an expression by merging terms that have the same variable elements raised to the same power. This step is essential for reducing the equation to a more manageable form and is a key component in simplifying and ultimately solving the equation.

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