Problem 86 Evaluate each expression for \(x... [FREE SOLUTION]

Chapter 5: Problem 86

Evaluate each expression for $x=6, y=0.3,$ and $z=-2.4 .$ $$ x-z $$

Short Answer

Expert verified

8.4

Step by step solution

Understand the Expression

The expression given is $x - z$. You need to substitute the values of $x$ and $z$ into this expression to solve it.

Substitute Known Values

Replace $x$ with 6 and $z$ with -2.4, so the expression becomes $6 - (-2.4)$.

Simplify the Expression

Simplifying $6 - (-2.4)$ involves changing subtraction of a negative number to addition: $6 + 2.4$.

Calculate the Result

Add 6 and 2.4 to get $8.4$.

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Key Concepts

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

Substitution in Expressions

In any mathematical expression, substitution is a crucial step. It involves replacing variables with their given values to simplify and solve the expression.
Let's take a closer look at how to do this.
When you see an expression like $x - z$, and you are given specific values for $x$ and $z$, substitution becomes straightforward:

Find the place in the expression where the variable appears.
Replace each instance of the variable with its given numerical value.

For instance, if $x = 6$ and $z = -2.4$, substitute these into the expression:
The expression $x - z$ becomes $6 - (-2.4)$.
As you can see, substitution is about following a set of instructions (the values) and applying them to the expression.

Negative Numbers

Understanding how negative numbers work is essential, especially when they're part of an expression.
Working with negative numbers might be confusing initially, but let鈥檚 demystify this.Negative numbers are numbers less than zero, which always have a minus \ sign in front of them.
For example, $-2.4$ is a negative number where 2.4 units are counted below zero.When you subtract a negative number, you effectively add its positive counterpart:

Subtraction of $-2.4$ is the same as adding $2.4$.
The operation $6 - (-2.4)$ transforms into $6 + 2.4$.

By understanding these rules, you can approach calculations with negative numbers with confidence.

Addition

Addition is the simple arithmetic process of combining two numbers to get their total.
You use this operator all the time, often without even realizing it.Once you've substituted the values into an expression and simplified it鈥攆or instance, changing $6 - (-2.4)$ to $6 + 2.4$鈥攁ddition is what you do next:

Stack the numbers on top of each other if necessary, to align their decimal points.
Add each digit starting from the rightmost side (the smallest place value).
Carry over any extra values to the next place value when needed.

So, adding $6$ and $2.4$ gets you $8.4$.
It's a straightforward way of obtaining the result after all the substitution and simplification steps.

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91影视

Evaluate each expression for \(x=6, y=0.3,\) and \(z=-2.4 .\) $$ x-z $$

Short Answer

Step by step solution

Understand the Expression

Substitute Known Values

Simplify the Expression

Calculate the Result

Key Concepts

Substitution in Expressions

Negative Numbers

Addition

One App. One Place for Learning.

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