Problem 397 Evaluate each expression. \(-2... [FREE SOLUTION]

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Chapter 1: Problem 397

Evaluate each expression. \(-2 x+17\) when (a) \(x=8\) (b) \(x=-8\)

Short Answer

Expert verified

(a) 1, (b) 33

Step by step solution

Substitute value in (a)

Substitute the value of \(x\) with \(8\) in the expression \(-2x + 17\). This gives us: \(-2(8) + 17\)

Simplify expression (a)

First, calculate \(-2 \times 8\) which is \(-16\). Then add \(17\) to \(-16\): \(-16 + 17 = 1\). So, when \(x = 8\), \(-2x + 17 = 1\).

Substitute value in (b)

Substitute the value of \(x\) with \(-8\) in the expression \(-2x + 17\). This gives us: \(-2(-8) + 17\)

Simplify expression (b)

First, calculate \(-2 \times -8\) which is \(16\). Then add \(17\) to \(16\): \(16 + 17 = 33\). So, when \(x = -8\), \(-2x + 17 = 33\).

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Key Concepts

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

Substitution

Substitution is a fundamental technique in algebra where you replace a variable with a specific value. It helps us evaluate expressions or solve equations.

In our exercise, we substituted the value of x with the given numbers.
For (a), we substituted x with 8:
\[ -2(8) + 17 \]
For (b), we substituted x with -8:
\[ -2(-8) + 17 \]
Always ensure the value is placed in the correct position, preserving the signs around it.
This step forms the basis for further simplification and solving.

Simplification

Simplification involves performing arithmetic operations to condense the expression. This step makes complex expressions easier to work with.

Let's break down the simplification process of our exercise step by step:
For (a), after substituting x = 8:
\[ -2 \times 8 = -16 \]
Adding 17 to -16, we get:
\[ -16 + 17 = 1 \]
For (b), after substituting x = -8:
\[ -2 \times -8 = 16 \]
Adding 17 to 16, we get:
\[ 16 + 17 = 33 \]
Simplification requires careful attention to arithmetic rules, especially with negative numbers and the order of operations.
This will ensure that you get accurate results.

Linear Equations

Linear equations are equations where the highest power of the variable is 1. They are straightforward and form the output as a line when graphed.

In our exercise, the linear equation given is:
\[ -2x + 17 \] \[ \]
We derived its value by substituting x and then simplifying.
Linear equations are fundamental in algebra to model relationships and predict values. They follow the standard form of:
\[ ax + b = c \]
where x is our variable, and a, b, and c are constants.
Understanding linear equations is the foundation for delving into more complex functions.
They are simple yet powerful tools for various algebra problems.

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91影视

Evaluate each expression. \(-2 x+17\) when (a) \(x=8\) (b) \(x=-8\)

Short Answer

Step by step solution

Substitute value in (a)

Simplify expression (a)

Substitute value in (b)

Simplify expression (b)

Key Concepts

Substitution

Simplification

Linear Equations

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