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Chapter 2: Problem 18

Determine whether inequality is satisfied by the given number. \(6-3 x \geq 10-2 x,-4\)

Short Answer

Expert verified
Yes, the inequality is satisfied by x = -4.

Step by step solution

01

Substitute the Given Number into the Inequality

First, substitute x = -4 into the inequality 6 - 3x and 10 - 2x.
02

Evaluate Each Expression

Calculate the value of 6 - 3(-4) and 10 - 2(-4). For 6 - 3(-4): 6 + 12 = 18 For 10 - 2(-4): 10 + 8 = 18.
03

Compare the Results

Next, compare the values to see if 18 is greater than or equal to 18. Since 18 = 18, the inequality is satisfied.

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Key Concepts

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

Substitution Method
The substitution method is used to replace variables with numbers to simplify expressions or solve equations.
In this inequality problem, we substitute the given number x = -4 into the inequality 6 - 3x to evaluate it.
By plugging in the value of x , we can break down the problem into simpler arithmetic operations.
This method makes it easier to handle complex expressions by turning them into basic calculations.
Evaluating Expressions
Evaluating expressions involves computing the value of an expression after substituting variables with given numbers.
Let's break down the calculations in this problem:
First, we substitute x = -4 into the expression 6 - 3x.
This gives us 6 - 3(-4).
We then follow the order of operations, multiplying -3 with -4 to get 12.
So, 6 + 12 = 18.
Next, we substitute x = -4 into 10 - 2x.
This gives us 10 - 2(-4).
Again, we multiply -2 with -4 to get 8.
So, 10 + 8 = 18.
Comparison of Values
Comparison of values involves seeing how different numbers relate to each other using comparison operators.
In this problem, we need to compare the evaluated expressions to determine if the inequality is satisfied.
After evaluating 6 - 3x and 10 - 2x, we obtained 18 for both.
To compare, we see if 18 is greater than or equal to 18.
Since 18 = 18, the inequality 6 - 3x is indeed satisfied.

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