To solve the inequality "Eight less than four times a number is less than 56," we will follow a step-by-step process. Let's denote the number by [tex]\( x \)[/tex].
The given inequality can be expressed as:
[tex]\[ 4x - 8 < 56 \][/tex]
### Step 1: Isolate the term involving [tex]\( x \)[/tex]
To eliminate the constant term on the left side of the inequality, we'll add 8 to both sides:
[tex]\[ 4x - 8 + 8 < 56 + 8 \][/tex]
[tex]\[ 4x < 64 \][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Next, we'll divide both sides of the inequality by 4 to isolate [tex]\( x \)[/tex]:
[tex]\[ \frac{4x}{4} < \frac{64}{4} \][/tex]
[tex]\[ x < 16 \][/tex]
### Conclusion
The inequality [tex]\( x < 16 \)[/tex] means that the possible values of [tex]\( x \)[/tex] are any number less than 16. Hence, the correct answer is [tex]\( x < 16 \)[/tex].
Among the provided choices:
- [tex]\( x > 12 \)[/tex]
- [tex]\( x < 12 \)[/tex]
- [tex]\( x < 16 \)[/tex]
- [tex]\( x > 16 \)[/tex]
The appropriate choice that matches our solution is:
[tex]\[ x < 16 \][/tex]
