This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Split the compound inequality into two separate inequalities. The given inequality is (1)/(2)(5x-4) x + 5(1)/(2) < 3x + 1(1)/(2). This can be written as: *a) (1)/(2)(5x-4) x + 5(1)/(2) *b) x + 5(1)/(2) < 3x + 1(1)/(2) Step 2: Solve the first inequality. (1)/(2)(5x-4) x + 5(1)/(2) Convert the mixed number to an improper fraction: 5(1)/(2) = (11)/(2). (1)/(2)(5x-4) x + (11)/(2) Multiply the entire inequality by 2 to eliminate fractions: 2 × (1)/(2)(5x-4) 2 × x + 2 × (11)/(2) 5x-4 2x + 11 Subtract 2x from both sides: 5x - 2x - 4 11 3x - 4 11 Add 4 to both sides: 3x 11 + 4 3x 15 Divide by 3: x 5 Step 3: Solve the second inequality. x + 5(1)/(2) < 3x + 1(1)/(2) Convert mixed numbers to improper fractions: 5(1)/(2) = (11)/(2) and 1(1)/(2) = (3)/(2). x + (11)/(2) < 3x + (3)/(2) Multiply the entire inequality by 2 to eliminate fractions: 2 × x + 2 × (11)/(2) < 2 × 3x + 2 × (3)/(2) 2x + 11 < 6x + 3 Subtract 2x from both sides: 11 < 6x - 2x + 3 11 < 4x + 3 Subtract 3 from both sides: 11 - 3 < 4x 8 < 4x Divide by 4: (8)/(4) < x 2 < x Step 4: Combine the solutions. From Step 2, we have x 5. From Step 3, we have x > 2. Combining these two conditions gives 2 < x 5. Step 5: Find the integral values of x. The integral values of x that are greater than 2 and less than or equal to 5 are 3, 4, and 5. The integral values are 3, 4, 5. 3 done, 2 left today. You're making progress.