/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 59 \(5-x=-2 x-11\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 59

\(5-x=-2 x-11\)

Short Answer

Expert verified
The solution is \( x = -16 \).

Step by step solution

01

Combine like terms

First, add \( x \) to both sides of the equation: \[ 5 - x + x = -2x - 11 + x \] which simplifies to \[ 5 = -x - 11 \].
02

Isolate the variable term

Next, add 11 to both sides of the equation: \[ 5 + 11 = -x - 11 + 11 \] which simplifies to \[ 16 = -x \].
03

Solve for x

Finally, multiply both sides by -1 to solve for \( x \): \[ -1 \times 16 = -1 \times -x \] which simplifies to \[ x = -16 \].

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Key Concepts

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

Combining Like Terms
When solving linear equations, one of the first steps is often to combine like terms. This means adding or subtracting terms on both sides of the equation that have the same variable part. In the given exercise \(5 - x = -2x - 11\), we start by simplifying the terms involving \(x\). To do this, we add \(x\) to both sides:
\[ 5 - x + x = -2x - 11 + x \] Now, combine like terms to get: \[ 5 = -x - 11 \] By performing this combination, we make the equation simpler and prepare for the next step, which is isolating the variable.
Isolating the Variable
Once like terms are combined, the next goal is to isolate the variable on one side of the equation. This helps us solve for the variable \(x\). In our example, we start with:
\[ 5 = -x - 11 \] To isolate \(x\), we need to move the constant term on the same side as \(x\). We do this by adding 11 to both sides:
\[ 5 + 11 = -x - 11 + 11 \] This simplifies to:
\[ 16 = -x \] Now, the variable term is isolated, and we can move on to solving for \(-x\).
Solving for x
The final step in solving the equation is to solve for the variable \(x\). At this stage, we have an equation where the variable is almost isolated:
\[ 16 = -x \] To solve for \(x\), we need to get rid of the negative sign in front of \(x\). We do this by multiplying both sides of the equation by \(-1\):
\[ -1 \times 16 = -1 \times -x \] Simplifying this, we get:
\[ -16 = x \] Therefore, \(x = -16\).
By following these steps鈥攃ombining like terms, isolating the variable, and solving for \(x\)鈥攚e successfully find the value of the variable in the equation. Remember, each step is crucial, and practicing these will help you solve linear equations more effortlessly.

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