Question

Solve the equation. $$3-\frac{3}{4} x=-6$$

   Solve the equation.
$$3-\frac{3}{4} x=-6$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 3, Problem 23

Instant Answer

Solved by Expert Raushan Kumar

09/27/2020

Step 1

This gives us: $$-\frac{3}{4}x = -6 - 3$$ Show more…

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Solve the equation. $$3-\frac{3}{4} x=-6$$

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Key Concepts

Balancing Equations

Balancing equations involves ensuring that both sides of an equation remain equal while performing arithmetic operations. It is based on the principle that the same operation must be applied to both sides of the equation. This principle is critical to maintaining the equality of the equation throughout the process of isolating and solving for the variable.

Clearing Fractions

Clearing fractions is a technique used to simplify equations that involve fractional coefficients or terms. This is typically achieved by multiplying both sides of the equation by the least common denominator (LCD), thereby eliminating the fractions and converting the equation into a form that is easier to manipulate. This step streamlines the process of isolating the variable.

Linear Equations

Linear equations are mathematical statements that equate two expressions and involve variables raised only to the first power. They represent straight lines when graphed on a coordinate plane and are solved by isolating the variable. Solving a linear equation typically involves operations such as addition, subtraction, multiplication, or division to manipulate the equation into a form where the variable stands alone on one side.

Inverse Operations

Inverse operations are steps used to 'undo' an operation on a variable, thereby isolating it in an equation. For example, if the variable is divided by a number, multiplication serves as the inverse operation to cancel the division, and vice versa. These operations are grounded in the principle of performing equal operations on both sides of an equation to maintain balance.

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