$$\frac{ x }{ 8 } - \frac{ x }{ 10 } > \frac{ x }{ 12 } -1$$
Solve for x
$x<\frac{120}{7}$
Solution Steps
Multiply both sides of the equation by $120$, the least common multiple of $8,10,12$. Since $120$ is positive, the inequality direction remains the same.
$$15x-12x>10x-120$$
Combine $15x$ and $-12x$ to get $3x$.
$$3x>10x-120$$
Subtract $10x$ from both sides.
$$3x-10x>-120$$
Combine $3x$ and $-10x$ to get $-7x$.
$$-7x>-120$$
Divide both sides by $-7$. Since $-7$ is negative, the inequality direction is changed.
$$x<\frac{-120}{-7}$$
Fraction $\frac{-120}{-7}$ can be simplified to $\frac{120}{7}$ by removing the negative sign from both the numerator and the denominator.
