Solve for X: Fraction Equation 4/(x+5) = 8/((2-x)×3)

Question

Solve for X:

$\frac{4}{x+5}=\frac{8}{(2-x)\times3}$

00:00 Find X

00:03 Multiply by common denominator to eliminate fractions

00:21 Carefully open parentheses properly, multiply by each factor

00:46 Arrange the equation so that X is isolated on one side

01:03 Combine like terms

01:10 Isolate X

01:14 Factor 16 into 4 and 4

01:21 Factor 20 into 5 and 4

01:27 Simplify as much as possible

01:32 And this is the solution to the problem

To solve the equation $\frac{4}{x+5} = \frac{8}{(2-x) \times 3}$ , we will use cross-multiplication.

Step 1: Set up the cross-multiplication: $4 \times (2-x) \times 3 = 8 \times (x+5)$
Step 2: Simplify the left side of the equation: $12(2-x) = 8(x+5)$
Step 3: Distribute on both sides: $24 - 12x = 8x + 40$
Step 4: Combine like terms. First, bring all terms involving $x$ to one side and constant terms to the other side: $24 - 40 = 8x + 12x$
Step 5: Simplify the equation: $-16 = 20x$
Step 6: Solve for $x$ by dividing both sides by 20: $x = -\frac{16}{20}$
Step 7: Simplify the fraction: $x = -\frac{4}{5}$

Therefore, the solution to the equation is $x = -\frac{4}{5}$ .

$-\frac{4}{5}$