Solve the Fraction Equation: Find X in 9/11 - 8/15x = 8/22

Question

Solve for X:

$\frac{9}{11}-\frac{8}{15}x=\frac{8}{22}$

00:00 Solve

00:03 We want to isolate the unknown X

00:08 We'll arrange the equation so that X is alone on one side

00:22 We'll reduce what we can

00:38 We'll break down 8 into factors 4 and 2, and 22 into factors 11 and 2

00:52 We'll reduce what we can

00:56 We'll write everything under one fraction

01:04 We'll isolate X and calculate

01:09 We'll multiply by the reciprocal fraction to eliminate the fraction

01:30 We'll reduce what we can

01:34 Negative times negative always equals positive

01:37 Make sure to multiply numerator by numerator and denominator by denominator

01:40 And this is the solution to the problem

To solve the equation $\frac{9}{11} - \frac{8}{15}x = \frac{8}{22}$ , follow these steps:

Step 1: Find the least common denominator (LCD) of 11, 15, and 22, which is 330.
Step 2: Multiply every term in the equation by 330 to eliminate the fractions:
$330 \times \frac{9}{11} - 330 \times \frac{8}{15}x = 330 \times \frac{8}{22}$ .
Step 3: Simplify each term:
- For $\frac{9}{11}$ : $330 \times \frac{9}{11} = 270$ ,
- For $\frac{8}{15}x$ : $330 \times \frac{8}{15}x = 176x$ ,
- For $\frac{8}{22}$ : $330 \times \frac{8}{22} = 120$ .
Step 4: Substitute back into the equation:
$270 - 176x = 120$ .
Step 5: Isolate $x$ :
- Subtract 270 from both sides: $-176x = 120 - 270$ ,
- Simplify: $-176x = -150$ ,
- Divide both sides by $-176$ : $x = \frac{-150}{-176} = \frac{75}{88}$ .

Thus, the value of $x$ is $\frac{75}{88}$ .

$\frac{75}{88}$