Question

Solve each equation. $$\frac{3 w-2}{6}=1-\frac{w-1}{3}$$

   Solve each equation.
 
$$\frac{3 w-2}{6}=1-\frac{w-1}{3}$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 2, Problem 33

Instant Answer

Solved by Expert Matthew Biollo

03/20/2021

Step 1

This gives us: $$6 \cdot \frac{3 w-2}{6}=6 \cdot 1-6 \cdot \frac{w-1}{3}$$ which simplifies to: $$3w - 2 = 6 - 2(w - 1)$$ Show more…

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Solve each equation. $$\frac{3 w-2}{6}=1-\frac{w-1}{3}$$

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Key Concepts

Linear Equations

A linear equation is an algebraic equation in one or more variables that forms a straight line when graphed. Solving such equations typically involves finding the value of the variable(s) that make the equation true, usually resulting in a single solution.

Clearing Fractions

Clearing fractions involves multiplying the entire equation by the least common denominator to eliminate fractional expressions. This step simplifies the equation into a form that is easier to manipulate and solve using standard algebraic techniques.

Combining Like Terms

Combining like terms is the process of simplifying an equation by merging terms that have the same variable factors. This reduces the complexity of the equation, making it easier to isolate the variable and solve the equation.

Isolating the Variable

Isolating the variable refers to rearranging the equation so that the variable of interest is on one side of the equation by itself. This typically involves applying operations such as addition, subtraction, multiplication, or division to both sides of the equation to solve for the variable.

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