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

1 answer

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: \[ x < \frac{9}{8} \]