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Chapter 8: Problem 114

Solve the equation for the variable. $$11 w+6=93$$

Short Answer

Expert verified
w = 7.909 or w = \frac{87}{11}

Step by step solution

01

Isolate the term with the variable

To isolate the term with the variable, subtract 6 from both sides of the equation:\(11w + 6 - 6 = 93 - 6\)
02

Simplify the equation

Simplify the left and right sides:\(11w = 87\)
03

Solve for the variable

Divide both sides by the coefficient of the variable (11):\(w = \frac{87}{11}\)
04

Simplify the solution

Simplify the fraction if possible. In this case, \(\frac{87}{11}\) simplifies to approximately 7.909, but can be written as a fraction:\(w = 7.909\) or \(w = \frac{87}{11}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the Variable
To solve linear equations, the first step usually involves isolating the term with the variable. This means we need to get the variable on one side of the equation by itself. In our exercise, the equation is:\(11w + 6 = 93\)To isolate the term with \(w\), subtract 6 from both sides, so:\(11w + 6 - 6 = 93 - 6\)This simplifies to:\(11w = 87\).
By isolating the variable, we make it easier to perform operations to find its value.
Simplify Equations
Simplifying equations is a crucial skill in algebra. It involves performing basic arithmetic operations to make the equation cleaner and more manageable. After isolating the variable term in our exercise, the equation became:\(11w = 87\)At this stage, the equation is simplified enough for the next steps, but sometimes you may need to simplify more complicated expressions before solving for the variable.
Solve for the Variable
Once the equation is simplified, the next step is to solve for the variable. This involves isolating the variable completely by performing the necessary operations.
To solve \(11w = 87\), divide both sides by 11:\(w = \frac{87}{11}\)By dividing by the coefficient of \(w\) (which is 11), we find our solution:\(w = 7.909\) or more accurately, we leave it as a fraction \(\frac{87}{11}\).
Solving for the variable allows us to find the actual value of the variable in the equation.
Fraction Simplification
Fraction simplification is an essential part of solving equations. It involves reducing a fraction to its simplest form. In our problem, the fraction \(\frac{87}{11}\) cannot be simplified further, but it can be converted to a decimal:\(w = 7.909\)It's important to recognize when a fraction can be simplified and when it's already in its simplest form. Knowing these skills helps in presenting your final answer accurately and clearly.

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