Question

Solve each equation. Check your solution. $$2 x-1=9$$

   Solve each equation. Check your solution.
$$2 x-1=9$$

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 5, Problem 80

Instant Answer

Solved by Expert Kyler Gray

07/16/2020

Step 1

We want to isolate the variable $x$, so we first get rid of the $-1$ on the left side. We do this by adding $1$ to both sides of the equation. This gives us: \[2x - 1 + 1 = 9 + 1\] which simplifies to: \[2x = 10\] Show more…

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Solve each equation. Check your solution. $$2 x-1=9$$

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Key Concepts

Linear Equations

A linear equation is an algebraic statement that equates an expression containing a variable raised to the first power to another expression. It typically has the general form ax + b = c, and solving these equations involves finding the value of the variable that satisfies the equality.

Isolation of the Variable

This concept involves rearranging the equation to obtain the variable of interest alone on one side. By performing equivalent operations on both sides of the equation, such as adding or subtracting terms and dividing or multiplying by coefficients, you can isolate the variable, making the solution apparent.

Inverse Operations

Inverse operations are paired mathematical operations that cancel each other out, such as addition and subtraction or multiplication and division. They are used in the process of isolating the variable in an equation, allowing you to undo operations applied to the variable in order to solve for it.

Checking the Solution

Once a solution is obtained, it is important to verify its correctness by substituting it back into the original equation. This process of checking ensures that the solution satisfies the equation, reaffirming the validity of the answer derived through algebraic manipulations.

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