a+8-2(a-12)>0
do you do distributive property?
a+8 -2a +12 > 0
-a + 20 > 0
i think
i got it already its
a + 8 - 2a + 24 > 0
-a + 32 > 0
32 > a, or a < 32
Yes, to solve the given inequality, it is necessary to apply the distributive property. Here's how you can do it step-by-step:
1. Start with the given inequality: a + 8 - 2(a - 12) > 0
2. Simplify the expression inside the parentheses: a + 8 - 2a + 24 > 0
3. Combine like terms: (a - 2a) + (8 + 24) > 0
4. Simplify further: -a + 32 > 0
5. To remove the negative sign from "-a", multiply both sides by -1 (remember to also change the inequality sign): (-1)(-a + 32) < (0)(-1)
This step is necessary because multiplying or dividing both sides of an inequality by a negative number flips the inequality sign.
6. Simplify: a - 32 < 0
7. Finally, solve for "a": Add 32 to both sides: (a - 32) + 32 < 0 + 32
8. Simplify: a < 32
Therefore, the solution to the inequality a + 8 - 2(a - 12) > 0 is a < 32.