Simplifying Algebraic Expressions: 2/11x - 5/4 ± 9/11x*5/4 + 1 3/4
In algebra, simplifying expressions is an essential skill to master. In this article, we will walkthrough the process of simplifying the expression 2/11x - 5/4 ± 9/11x*5/4 + 1 3/4.
Step 1: Simplify the fraction 1 3/4
The mixed fraction 1 3/4 can be simplified by converting it to an improper fraction. To do this, we multiply the whole number part (1) by the denominator (4) and add the numerator (3):
1 3/4 = (1 × 4 + 3) / 4 = 7/4
Step 2: Simplify the expression 2/11x - 5/4
To simplify this expression, we can start by finding a common denominator between the two fractions. The least common multiple (LCM) of 11 and 4 is 44. So, we can rewrite the expression as:
2/11x - 5/4 = (2x × 4) / 44 - (5 × 11) / 44 = (8x - 55) / 44
Step 3: Simplify the expression 9/11x*5/4
To simplify this expression, we can multiply the numerators and denominators separately:
9/11x * 5/4 = (9x × 5) / (11 × 4) = 45x / 44
Step 4: Combine the simplified expressions
Now, we can combine the simplified expressions:
(8x - 55) / 44 ± 45x / 44 + 7/4
To add or subtract fractions with the same denominator, we can add or subtract the numerators and keep the denominator:
= (8x - 55 ± 45x) / 44 + 7/4 = (8x ± 45x - 55) / 44 + 7/4
Final Simplification
Finally, we can combine like terms:
= (53x - 55) / 44 + 7/4
And that's the simplified form of the given expression!
