Problem 28 Solve the given equation for \(x... [FREE SOLUTION]

91影视

Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 1: Problem 28

Solve the given equation for $x$. $$ 1+x=16 $$

Short Answer

Expert verified

The solution is $x = 15$.

Step by step solution

Understand the Problem

We need to solve the equation $1 + x = 16$ for $x$. This means we want to find the value of $x$ that makes the equation true.

Isolate Variable x

To isolate $x$, we need to remove the constant term $1$ from the left side of the equation. We can do this by subtracting $1$ from both sides of the equation. This gives us $1 + x - 1 = 16 - 1$.

Simplify Both Sides of the Equation

Simplifying both sides of the equation, we have $x = 15$. This is the solution to the equation.

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Key Concepts

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

Isolating the Variable

When solving an equation, our main goal is to "isolate the variable" we are interested in. This means we want to get the variable, which is "x" in this case, alone on one side of the equation. Why? Because when "x" is by itself, we can directly see its value.

To isolate the variable, we need to perform operations that will eliminate any other numbers around it. In our example, the equation is $1 + x = 16$. We have added "1" to "x." To cancel out this "1," we use subtraction.

We subtract "1" from both sides: $1 + x - 1 = 16 - 1$.
This leaves us with just "x" on one side: $x = 15$.

This process of removing numbers to leave the variable by itself is essential in solving equations.

Constant Term

A constant term is a number in an equation that does not change; it doesn't contain any variables. In our problem, the constant term is "1," which is part of the expression $1 + x$.

Understanding constant terms is important because they are what we need to get rid of in the process of isolating the variable.

In the equation $1 + x = 16$, the "1" is a constant term that needs to be subtracted to help isolate "x."
Once subtracted, it effectively removes itself from the equation: $1 + x - 1 = 16 - 1$.

Being able to identify and correctly deal with constant terms can make solving equations much smoother and easier.

Simplifying Equations

Simplifying equations involves reducing the equation into its simplest form. This means performing operations that make the equation easier to work with or completely solving for the variable.

Once we have subtracted the constant $1$ from both sides of our equation $1 + x = 16$, we simplify the result:

On the left, $1 - 1$ leaves us $x$.
On the right, $16 - 1$ leaves us $15$.

Hence, the simplified equation $x = 15$ clearly shows the solution. Simplifying helps in easily interpreting the final value of "x" without extra complexities.

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91影视

Solve the given equation for \(x\). $$ 1+x=16 $$

Short Answer

Step by step solution

Understand the Problem

Isolate Variable x

Simplify Both Sides of the Equation

Key Concepts

Isolating the Variable

Constant Term

Simplifying Equations

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