Problem 15 Solve the inequality. $$x+5&gt... [FREE SOLUTION]

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Chapter 6: Problem 15

Solve the inequality. $$x+5>-13$$

Short Answer

Expert verified

The solution to the inequality $x+5 > -13$ is $x > -18$.

Step by step solution

Identify the equation

The inequality given to solve is $x+5 > -13$.

Isolate the variable

Subtract 5 from both sides to isolate $x$ on the left side of the inequality. So, $x+5-5 > -13-5$, which simplifies to $x > -18$.

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Key Concepts

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

Understanding Inequalities

Inequalities are mathematical expressions showing that two values are not equivalent. Unlike equations, which show two quantities as equal, inequalities show a range of possible solutions. They use symbols such as:

$>$ (greater than)
$<$ (less than)
$\geq$ (greater than or equal to)
$\leq$ (less than or equal to)

Understanding these signs is important. They help us know whether one side is larger or smaller and by how much.
For instance, in the inequality $x + 5 > -13$, we want to find all values of $x$ that make the statement true. This tells us that $x$ plus 5 should be more than $-13$.
It also means any number for $x$ that satisfies this rule would be correct.

How to Isolate a Variable

Isolating a variable is a key skill in solving inequalities or equations. It means getting the unknown variable by itself on one side of the inequality sign. This is often done by performing inverse operations.
Think of inverse operations as undoing what was originally done:

To undo addition, we subtract.
To undo subtraction, we add.
To undo multiplication, we divide.
To undo division, we multiply.

For the inequality $x + 5 > -13$, we start by removing the 5 that is added to $x$.
We do this by subtracting 5 from both sides, giving you this new inequality: $x > -18$.
By isolating $x$, we have found a simpler form that tells us any $x$ greater than $-18$ will satisfy the inequality.

The Role of Algebra in Solving Inequalities

Algebra provides tools to solve problems involving unknowns like inequalities. It allows us to find solutions systematically.
Besides isolating variables, algebra also involves simplifying expressions and understanding the properties of numbers.
While dealing with inequalities, remember:

Keep both sides balanced by performing the same operation on each side.
The inequality sign flips direction when multiplying or dividing by a negative number.

In the solved inequality $x > -18$, there were no negative multiplications or divisions involved. Thus, the direction of the sign remained unchanged.
Practicing algebra not only helps in isolating variables but also builds a strong foundation for more complex mathematical concepts.

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91影视

Solve the inequality. $$x+5>-13$$

Short Answer

Step by step solution

Identify the equation

Isolate the variable

Key Concepts

Understanding Inequalities

How to Isolate a Variable

The Role of Algebra in Solving Inequalities

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