Question

Solve each equation. Check your solution. $$5 r+3 r-6=10$$

   Solve each equation. Check your solution.
$$5 r+3 r-6=10$$

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 3, Problem 38

Instant Answer

Solved by Expert Amanda Stone

06/01/2020

Step 1

To do this, we add 6 to both sides of the equation: \[5r + 3r - 6 + 6 = 10 + 6\] This simplifies to: \[5r + 3r = 16\] Show more…

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Solve each equation. Check your solution. $$5 r+3 r-6=10$$

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Key Concepts

Checking the Solution

Checking the solution means substituting the found value back into the original equation to verify that it satisfies the equation. This step is crucial as it confirms the accuracy of the solution and ensures that no errors were made during the process.

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. They have a degree of one, meaning that the variable is only raised to the first power, and their solutions typically involve finding the value of the variable that satisfies the equality.

Combining Like Terms

Combining like terms is a process used to simplify an equation or expression by adding or subtracting terms that have the same variable part. This step simplifies the structure of the equation, making it easier to isolate the variable and solve for it.

Isolating the Variable

Isolating the variable involves manipulating an equation to get the variable of interest on one side and all constants on the other. This usually includes operations such as addition, subtraction, multiplication, or division to undo the operations affecting the variable, leading to its explicit value.

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