Question

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

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

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 0, Problem 21

Instant Answer

Solved by Expert Ankit Gupta

07/24/2020

Step 1

We can do this by adding $3x$ to both sides of the equation. This gives us: $$-3x - 3 + 3x = 5x - 3 + 3x$$ which simplifies to: $$-3 = 8x - 3$$ Show more…

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

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Key Concepts

Linear Equation

A linear equation is an algebraic expression that represents a straight line when graphed and typically involves variables raised only to the first power. It serves as a foundational concept in algebra, where the goal is to find the value of the variable that makes the equation true.

Algebraic Manipulation

Algebraic manipulation involves the systematic use of operations such as addition, subtraction, multiplication, and division to modify equations. This process is essential for rearranging equations in order to isolate the unknown variable and simplify the problem to a solvable form.

Properties of Equality

The properties of equality guarantee that if the same operation is applied to both sides of an equation, the equality is maintained. This principle is crucial for justifying each manipulation step while solving equations.

Combining Like Terms

Combining like terms is a technique used to simplify equations by merging terms that have the same variable components. This consolidation helps in reducing the complexity of the equation and makes further manipulations more straightforward.

Isolating the Variable

Isolating the variable is the process of rearranging an equation so that the variable of interest is on one side, while all the constants are on the other. This step is key to finding the solution to an equation, as it ultimately provides the value of the unknown variable.

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