Question

What is the value of x

Answer 1

Given: (3x+2)/7 + (4(x+1))5 = (2(2x+1))/3

To find: The value of x.

Solution:

To find the value of x, first, the denominators are made equal by taking the L.C.M. of them.

$\frac{3x+2}{7} + \frac{4(x+1)}{5} = \frac{2}{3} (2x+1)$

$\frac{45x + 30 + 84x + 84}{105} = \frac{140x + 70}{105}$

Since both the sides of the equation have the same denominator now, they can be cancelled out.

$45x + 30 + 84x + 84=140x + 70$

The equation can be rearranged by shifting all the x terms on one side of the equation and all the constants on the other side of the equation.

$140x - 85x - 45x = 84 + 30 - 70$

$10x = 44$

$x = 4.4$

Therefore, the value of x is 4.4.

Answer 2

Answer: x = 4

Step-by-step explanation:

Given : $\frac{3x + 2}{7} + \frac{4(x + 1)}{5} = \frac{2}{3}(2x + 1)$

To find : Value of x

Solution :

⇒ $\frac{3x + 2}{7} + \frac{4(x + 1)}{5} = \frac{2}{3}(2x + 1)$

⇒ $\frac{5(3x + 2) + 28(x + 1)}{35} = \frac{2(2x + 1)}{3}$

⇒ $\frac{15x + 10 + 28x + 28}{35} = \frac{4x + 2}{3}$

⇒ $\frac{43x + 38}{35} = \frac{4x + 2}{3}$

⇒ $129x + 114 = 140x + 70$

⇒ $44 = 11x$

∴ $x = 4$

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