Question

Solve each equation. See Examples 1 and 2. $$9 x+11=7 x+1$$

   Solve each equation. See Examples 1 and 2.
$$9 x+11=7 x+1$$

Precalculus

Margaret L. Lial,… 6th Edition

Chapter 1, Problem 12

Instant Answer

Solved by Expert Julie Silva

04/17/2021

Step 1

This gives us: \[9x - 7x + 11 = 1\] which simplifies to: \[2x + 11 = 1\] Show more…

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Solve each equation. See Examples 1 and 2. $$9 x+11=7 x+1$$

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Key Concepts

Linear Equations

Linear equations are algebraic expressions where each term is either a constant or the product of a constant and a single variable. Solving these equations involves finding the value of the variable that makes the equation true, and it typically results in a single solution when there is one variable.

Combining Like Terms

Combining like terms is a process used to simplify algebraic expressions by summing coefficients of terms that have identical variable parts. This step is essential in solving linear equations as it reduces the equation to a simpler form, making it easier to isolate the variable.

Properties of Equality

The properties of equality allow us to perform the same operation on both sides of an equation without changing the equality's truth. These properties include the addition, subtraction, multiplication, and division properties and are crucial for manipulating and solving equations correctly.

Isolating the Variable

Isolating the variable involves rearranging the equation so that the variable is by itself on one side of the equation. This typically requires combining like terms and using inverse operations, following the properties of equality, to solve for the variable.

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