Answer :
Let's tackle this problem in two parts:
- Simplifying the inequality [tex]\frac{1}{4}x - 2 > 6[/tex]:
First, isolate [tex]x[/tex] by adding 2 to both sides of the inequality:
[tex]\frac{1}{4}x - 2 + 2 > 6 + 2[/tex]
This simplifies to:
[tex]\frac{1}{4}x > 8[/tex]
Next, to get rid of the fraction, multiply both sides by 4:
[tex]4 \cdot \frac{1}{4}x > 8 \cdot 4[/tex]
This gives:
[tex]x > 32[/tex]
So, the solution to the inequality is [tex]x > 32[/tex].
- Calculating [tex]6^2 - 4 \times 12 + 8[/tex]:
First, evaluate the exponent and multiplication:
[tex]6^2 = 36[/tex]
[tex]4 \times 12 = 48[/tex]
Substitute these values back into the expression:
[tex]36 - 48 + 8[/tex]
Now, perform the operations from left to right:
[tex]36 - 48 = -12[/tex]
[tex]-12 + 8 = -4[/tex]
Therefore, the result of the expression is [tex]-4[/tex].
