1) The first step is to find the Least Common Denominator (LCD) of <span>3/8,1/8,1/3,1/4
</span>⇒ Start Listing Multiples
List out all multiples of each denominator, and find the first common one.
8: <span><span>8,16,24</span> </span> 8 : <span>8,16,24 </span> 3 : <span>3,6,9,12,15,18,21,24 </span> 4 : <span><span>4,8,12,16,20,24</span> </span> Therefore, the LCD is <span>24
</span>⇒ By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
8 : <span>2,2,2</span> 8 : <span>2,2,2</span> 3 : 3 4 : <span><span>2,2</span> </span> Therefore, the LCD is <span>2×2×2×3=24
</span>Make the denominators the same as the LCD <span><span><span>3×3 / </span><span>8×3 </span></span>+<span><span>1×3 / </span><span>8×3 </span></span>−<span><span>1×8 / </span><span>3×8 </span></span>+<span><span>1×6 / </span><span>4×6
</span></span></span>Simplify. Denominators are now the same <span><span>9 / 24</span>+<span>3 / 24</span>−<span>8 / 24</span>+<span>6 / 24
</span></span>Join all the denominators <span><span>9+3−8+6 / </span>24
These 4 inequalities will be solved the same way we solve equations. We take variables to one side and numbers to another and use algebra to solve. Each of them are solved shown below:
1.
so x is greater than 4, we can write (variable first):
