Solve each equation. Provide reasons for each step. Check the answer. (3)/(4) x-17=20

Name: Problem 58, Chapter 1: Intermediate Algebra: Connecting Concepts through Applications
Uploaded: 2022-02-25T20:08:02-08:00
Duration: 2 min 10 s
Channel: Alison Rodriguez
Description: Solve each equation. Provide reasons for each step. Check the answer. (3)/(4) x-17=20

Solve each equation. Provide reasons for each step. Check...

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Key Concepts

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 variable raised to the first power. Solving these equations involves finding the value of the variable that makes the equation true, which typically means isolating the variable on one side of the equation.

Inverse Operations

Inverse operations are the mathematical operations that reverse the effect of another operation. In solving equations, they are essential for isolating the variable; for example, adding the opposite of a number cancels subtraction, and multiplying by the reciprocal cancels a multiplication by a fraction.

Multiplication by the Reciprocal

When a variable is multiplied by a fraction, using the reciprocal of that fraction is an effective method to isolate the variable. Multiplying both sides of the equation by the reciprocal cancels out the fractional coefficient, leaving the variable on one side of the equation.

Checking Solutions

Verifying or checking a solution involves substituting the value obtained back into the original equation to ensure that it satisfies the equation. This step is important as it confirms that the solution is correct and that no errors were made during the process of solving the equation.