Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for 
x. Express your answer as a proper or improper fraction in simplest terms.

(5)/(11)x-(1)/(4)=(1)/(2)
Answer: 
x=

Solve for x x . Express your answer as a proper or improper fraction in simplest terms.\newline511x14=12 \frac{5}{11} x-\frac{1}{4}=\frac{1}{2} \newlineAnswer: x= x=

Full solution

Q. Solve for x x . Express your answer as a proper or improper fraction in simplest terms.\newline511x14=12 \frac{5}{11} x-\frac{1}{4}=\frac{1}{2} \newlineAnswer: x= x=
  1. Isolate x term: First, we need to isolate the term containing xx on one side of the equation. To do this, we will add (1/4)(1/4) to both sides of the equation to move the constant term to the right side.\newline(5/11)x(1/4)+(1/4)=(1/2)+(1/4)(5/11)x - (1/4) + (1/4) = (1/2) + (1/4)
  2. Simplify right side: Now, we simplify the right side of the equation by finding a common denominator and adding the fractions (12)(\frac{1}{2}) and (14)(\frac{1}{4}). The common denominator for 22 and 44 is 44, so we convert (12)(\frac{1}{2}) to (24)(\frac{2}{4}) and then add it to (14)(\frac{1}{4}). (24)+(14)=(34)(\frac{2}{4}) + (\frac{1}{4}) = (\frac{3}{4}) So, the equation now is: (511)x=(34)(\frac{5}{11})x = (\frac{3}{4})
  3. Divide by coefficient: Next, we need to solve for xx by dividing both sides of the equation by (5/11)(5/11), which is the coefficient of xx. To divide by a fraction, we multiply by its reciprocal. The reciprocal of (5/11)(5/11) is (11/5)(11/5). So, we multiply both sides of the equation by (11/5)(11/5): (11/5)×(5/11)x=(3/4)×(11/5)(11/5) \times (5/11)x = (3/4) \times (11/5)
  4. Simplify and solve: We simplify both sides of the equation. On the left side, (115)(\frac{11}{5}) and (511)(\frac{5}{11}) cancel each other out, leaving us with xx. On the right side, we multiply the numerators and the denominators:\newlinex=3×114×5x = \frac{3 \times 11}{4 \times 5}\newlinex=3320x = \frac{33}{20}

More problems from Find the roots of factored polynomials