Question

Solve the equation. $$ -\frac{3}{4} x=21 $$

   Solve the equation.
$$
-\frac{3}{4} x=21
$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 6, Problem 62

Instant Answer

Solved by Expert Amy Jiang

09/03/2020

Step 1

To do this, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which is -4/3. This gives us: $$ x = 21 \times -\frac{4}{3} $$ Show more…

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Solve the equation. $$ -\frac{3}{4} x=21 $$

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Key Concepts

Operations with Rational Numbers

Operations with rational numbers involve performing arithmetic on fractions, such as multiplication, division, addition, and subtraction. Mastering these operations is crucial for working with equations that include fractional coefficients, ensuring accurate manipulation and simplification of the expressions.

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. The primary goal in solving a linear equation is to isolate the variable on one side of the equation, which leads to finding its value.

Inverse Operations

Inverse operations are used to undo the operations applied to the variable. For instance, if a variable is multiplied by a constant, dividing by that constant will cancel the multiplication, and vice versa. These operations are fundamental in the process of rearranging and solving equations.

Multiplicative Inverse

The multiplicative inverse of a number is the number that, when multiplied by the original number, yields 1. This concept is essential when dealing with equations that include fractional coefficients, as multiplying by the multiplicative inverse can eliminate the fraction and simplify the equation.

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