Question

What is the value of x in the equation 4 . 10 X+52 3 +35x+1 5 ?:)​

Answer 1

Answer:

$x=-3$

Step-by-step explanation:

Given:

$4\frac{3}{10}-(2\frac{2}{5}x+5\frac{1}{2})=\frac{1}{2}(-3\frac{3}{5}x+1\frac{1}{5})$

Distribute to remove parentheses:

$4\frac{3}{10}-2\frac{2}{5}x-5\frac{1}{2}=-\frac{18}{10}x+\frac{6}{10}$

For simplification and clarity, reduce all mixed numbers to simplified common fractions:

$\frac{43}{10}-\frac{12}{5}x-\frac{11}{2}=-\frac{9}{5}x+\frac{3}{5}$

Combine like terms:

$-\frac{12}{5}x-\frac{6}{5}=-\frac{9}{5}x+\frac{3}{5}$

Add 6/5 to both sides, then add 9/5x to both sides:

$-\frac{3}{5}x=\frac{9}{5}$

Divide both sides by -3/5 to isolate x (recall dividing by a number is equal to multiplying by its reciprocal):

$x=\frac{9}{5}\cdot -\frac{5}{3}, \\x=\frac{-9}{3},\\x=\boxed{-3}$