Question

Solve each equation. $$ 6+\frac{v}{-8}=\frac{4}{7} $$

   Solve each equation.
$$
6+\frac{v}{-8}=\frac{4}{7}
$$

Algebra 1 Common Core

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 2, Problem 45

Instant Answer

Solved by Expert Susan Matthias

06/18/2020

Step 1

Step 1: Multiply both sides of the equation by 56 (the least common denominator) to eliminate the fractions: $$ 56 \cdot (6+\frac{v}{-8}) = 56 \cdot \frac{4}{7} $$ This simplifies to: $$ 336 - 7v = 32 $$ Show more…

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Solve each equation. $$ 6+\frac{v}{-8}=\frac{4}{7} $$

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Key Concepts

Fraction Arithmetic

Fraction arithmetic involves performing operations such as addition, subtraction, multiplication, and division on fractions. A solid understanding of handling fractions is important because many equations involve fractional expressions, and manipulating these expressions correctly is key to reaching the solution.

Clearing Fractions

Clearing fractions refers to the process of eliminating fractional terms from an equation by multiplying both sides by a common denominator. This step simplifies the equation, making it easier to solve by reducing the complexity of the fraction operations involved.

Linear Equations

Linear equations are algebraic expressions set equal to a constant or another expression where the variable is of the first degree. The goal is to determine the value of the variable that satisfies the equality. This concept forms the basis for solving equations by applying systematic operations to isolate the variable.

Inverse Operations

Inverse operations are techniques used to reverse the effects of mathematical operations. In the context of solving equations, operations such as addition, subtraction, multiplication, and division are reversed in order to isolate the variable. This process is essential for systematically unraveling the steps applied to the variable.

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