To create an inequality that accurately represents the given verbal description, let's break down the description step-by-step:
1. Verbal Description: "The product of ten and a number is greater than the difference of four times the number and two."
2. Identify the number:
- Let [tex]\( x \)[/tex] represent the number.
3. Translate each part of the description into algebraic expressions:
- "The product of ten and a number" translates to [tex]\( 10x \)[/tex].
- "The difference of four times the number and two" translates to [tex]\( 4x - 2 \)[/tex].
4. Set up the inequality:
- According to the description, the product mentioned [tex]\( 10x \)[/tex] is greater than the difference [tex]\( 4x - 2 \)[/tex].
- Therefore, the inequality is: [tex]\( 10x > 4x - 2 \)[/tex].
Among the given options, the inequality that matches this description is:
- Option D: [tex]\( 10x > 4x - 2 \)[/tex]
Thus, the correct inequality is:
[tex]\[ 10x > 4x - 2 \][/tex]
Next, if we simplify this inequality:
1. Subtract [tex]\( 4x \)[/tex] from both sides to isolate the variable term:
[tex]\[ 10x - 4x > -2 \][/tex]
[tex]\[ 6x > -2 \][/tex]
2. You may stop here as this already shows the inequality in a simpler form. For further numerical steps, you might want to solve for [tex]\( x \)[/tex], but stopping at the simplified form is usually sufficiently indicative.
The correct inequality representing the verbal description is:
[tex]\[ 10x > 4x - 2 \][/tex]
