Answer:
[tex]x = \boxed{4}[/tex]
Step-by-step explanation:
What is cross multiplication?
Cross multiplication is a technique used to remove denominators from fractions in an equation
Given an equation where you have a fraction with an unknown variable, say x on the left side and a fraction with the same unknown variable x on the right side, the technique is as follows
- multiply the numerator of the left side with the denominator of the right side
- multiply the numerator of the right side with the denominator of the left side
- this will get rid of the denominator on both sides
- then you can use standard equation solving techniques to solve for x
The given equation is
[tex]\dfrac{3x}{4} = \dfrac{2x+7}{5}\\\\\text{Multiply left side numerator, 3x by 5 and right side numerator 2x + 7 by 4}\\\implies 3x \cdot 5 = (2x + 7) \cdot 4\\\\\implies 15x = 2x\cdot 4 + 7 \cdot 4\\\\\implies 15x = 8x + 28\\\\\text{Subtract 8x from both sides:}\\15x - 8x = 8x - 8x + 28\\\\7x = 28\\\\\text{Divide by 7 both sides:}\\x = 28/7\\x = 4\\[/tex]
