Solve each equation, and check the solution. (x-10)/(5)+(2)/(5)=-(x)/(3)

Name: Problem 63, Chapter 1: Algebra for College Students
Uploaded: 2022-02-11T18:15:10-08:00
Duration: 2 min 42 s
Channel: Avinash Vishwakarma
Description: Solve each equation, and check the solution. (x-10)/(5)+(2)/(5)=-(x)/(3)

step 1 In this problem, we have to solve this equation x minus 10 by 5 plus 2 by 5 equal minus x by 3.

Solve each equation, and check the solution....

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Key Concepts

Linear Equations

Linear equations are algebraic expressions where the highest power of the variable is 1. Solving these requires isolating the variable on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division.

Clearing Denominators

When an equation involves fractions, it is often simplified by clearing the denominators. This is achieved by multiplying each term by the least common denominator (LCD), which eliminates the fractions, making the equation easier to solve.

Operations with Fractions

Manipulation of fractions—including addition, subtraction, multiplication, and division—is a critical skill for solving equations that contain fractional expressions. It involves finding common denominators and simplifying the expressions to combine like terms effectively.

Checking Solutions

After finding a potential solution to an equation, substituting it back into the original equation verifies its correctness. This step is essential to ensure that the solution obtained does not lead to any contradictions or false statements, confirming the solution's validity.

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