Final answer:
To solve the inequality 1/2 (4x - 3) - 1/8 (5x -3) >= 1, distribute the fractions, combine like terms, and isolate x. The solution to the inequality is x ≥ 1.5455, meaning x is greater than or equal to approximately 1.5455.
Step-by-step explanation:
To solve the inequality 1/2 (4x - 3) - 1/8 (5x -3) ≥ 1, we start by distributing the fractions across the parentheses and then combining like terms.
First, distribute the 1/2 and 1/8:
1/2 × 4x - 1/2 × 3 - 1/8 × 5x + 1/8 × 3 ≥ 1
This simplifies to:
2x - 1.5 - 0.625x + 0.375 ≥ 1
Combine like terms:
2x - 0.625x - 1.5 + 0.375 ≥ 1
1.375x - 1.125 ≥ 1
Add 1.125 to both sides:
1.375x ≥ 2.125
Divide both sides by 1.375 to isolate x:
x ≥ 2.125 / 1.375 ≥ 1.5455 ... (approximately)
So the solution to the inequality is x ≥ 1.5455 or, in other words, x is any number greater than or equal to approximately 1.5455.
To solve the inequality 1/2 ( 4x - 3) - 1/8 ( 5x -3) ≥ 1, we first simplify the expression on the left side. Multiplying the fractions by their respective denominators, we get 2 ( 4x - 3) - ( 5x - 3)/8 ≥ 1. Simplifying further, we have 8( 4x - 3) - (5x - 3) ≥ 8. Distributing, we get 32x - 24 - 5x + 3 ≥ 8. Combining like terms, we have 27x - 21 ≥ 8. Adding 21 to both sides, we get 27x ≥ 29. Finally, dividing by 27, we find that x ≥ 29/27.