Step 1: Find the common denominator The denominator is $x(2x + 3)$. Rewrite: \[ \frac{4(2x + 3) - 5x}{x(2x + 3)} = 3. \] Step 2: Simplify the numerator \[ \frac{8x + 12 - 5x}{x(2x + 3)} = 3 \implies \frac{3x + 12}{x(2x + 3)} = 3. \] Step 3: Cross-multiply \[ 3x + 12 = 3x(2x + 3) \implies 3x + 12 = 6x^2 + 9x. \] Rearrange: \[ 6x^2 + 6x - 12 = 0. \] Simplify: \[ x^2 + x - 2 = 0. \] Step 4: Solve the quadratic equation Factorize: \[ x^2 + x - 2 = (x + 2)(x - 1) = 0. \] \[ x = -2 \quad \text{or} \quad x = 1. \] Step 5: Check solutions For $x = -2$, $2x + 3 = -1$, so the denominator is undefined. Therefore, $x = -2$ is not valid. Correct Answer: $x = 1$.
A shopkeeper sells an item at a 20 % discount on the marked price and still makes a 25 % profit. If the marked price is 500 rupees, what is the cost price of the item?
Select TRUE statements about lymph from the following:
A. Lymph vessels carry lymph through the body and finally open into larger arteries.
B. Lymph contains some amount of plasma, proteins and blood cells.
C. Lymph contains some amount of plasma, proteins and red blood cells.
D. Lymph vessels carry lymph through the body and finally open into larger veins.
The true statements are: