Respuesta :
Answer:
Option b is correct.
The given expression is an fractional equation.
Step-by-step explanation:
Given the expression: [tex]45x - \frac{24}{4} = 10x-\frac{7}{2}[/tex]
The fraction terms have denominator of 4 and 2.
The LCM of these number is, 4.
Multiply both sides of an equation by 4.
[tex]4(45x - \frac{24}{4}) = 4(10x-\frac{7}{2})[/tex]
Distribute on both sides we get;
[tex]180x - 24 = 40x - 14[/tex]
Add 24 both sides we have;
[tex]180x - 24 +24= 40x - 14 + 24[/tex]
Simplify:
[tex]180x = 40x +10[/tex]
Subtract 40x on both sides we get;
[tex]180x -40x = 40x +10- 40x[/tex]
Simplify:
[tex]140x =10[/tex]
Divide 140 on both sides we get, the solution
[tex]x = \frac{1}{14}[/tex]
The expression as an equation containing fractions, a fractional equation is [tex]\rm x=\dfrac{1}{14}[/tex].
Given
Expression; [tex]\rm 45x-\dfrac{24}{4} = 10x-\dfrac{7}{2}[/tex]
What is the fractional equation?
The equation which contains an unknown denominator and more terms is known as the fractional equation.
To solve the fractional equation follow all the steps given below.
- Step1; Taking LCM and simplifying both sides.
[tex]\rm45x- \dfrac{24}{4} = 10x-\dfrac{7}{2}\\\\\rm \dfrac{180x-24}{4} = \dfrac{20x-7}{2}[/tex]
- Step2; Apply cross multiplication.
[tex]\rm\dfrac{180x-24}{4} = \dfrac{20x-7}{2}\\\\2(180x-24) = 4(20x-7)\\\\360x-48=80x-28x[/tex]
- Step3; Taking all the terms right-hand side and simplifying the equation.
[tex]\rm 360x-48=80x-28\\\\360x-48-80x+28=0\\\\ 360x-80x-48+28=0\\\\ 280x-20=0\\\\280x=20\\\\x=\dfrac{20}{280}\\\\x = \dfrac{2}{28}\\\\x = \dfrac{1}{14}[/tex]
Hence, the expression as an equation containing fractions, a fractional equation is [tex]\rm x=\dfrac{1}{14}[/tex].
To know more about Fractions click the link given below.
https://brainly.com/question/5041896
