34 1\2>8x+25 1\2

Answer 1

To solve the inequality $34\frac{1}{2}>8x+25\frac{1}{2}$, we first convert the mixed numbers into improper fractions or decimals for easier manipulation.

1. Convert $34\frac{1}{2}$: $$34\frac{1}{2}=34+\frac{1}{2}=\frac{68}{2}+\frac{1}{2}=\frac{69}{2}$$

2. Convert $25\frac{1}{2}$: $$25\frac{1}{2}=25+\frac{1}{2}=\frac{50}{2}+\frac{1}{2}=\frac{51}{2}$$

Now, let's rewrite the inequality: $$\frac{69}{2}>8x+\frac{51}{2}$$

Next, we can eliminate the fractions by multiplying the entire inequality by 2: $$69>16x+51$$

Now we will isolate $x$:

1. Subtract 51 from both sides: $$69-51>16x$$ $$18>16x$$

2. Divide both sides by 16: $$\frac{18}{16}>x$$ $$\frac{9}{8}>x$$ or equivalently, $$x<\frac{9}{8}$$

Thus, the solution to the inequality is: $$x<\frac{9}{8}$$