Question

5(a-1)-9(a-2)=-3(2a+1)-2 Please solve and show work so that I can understand how to do the problem.

Answer 1

Hello!


Let's solve it step by step: Find the value of "a"

$5(a - 1) - 9(a - 2) = - 3(2a + 1) - 2$

Solving:
1º Pass: Delete the parentheses, effecting the distributive property, multiply the number of outside the parentheses with the ones inside, not forgetting to make the signal game.

$5a - 5 - 9a + 18 = - 6a - 3 - 2$

2º Pass: Put the numbers with letter to the left of the equality and the numbers without letter to the right of the equality, remembering that, changes the signal when changing sides.

$5a - 9a + 6a = - 3 - 2 + 5 - 18$

3º Pass: Perform the following operations

$- 4a + 6a = - 5 + 5 - 18$
$2a = 0 - 18$
$2a = - 18$
$a = \frac{-18}{2}$
$\boxed{\boxed{a = - 9}}\end{array}}\qquad\quad\checkmark$

Answer:
$\boxed{\boxed{a = - 9}}\end{array}}\qquad\quad\checkmark$

Note: Taking the truth (substitute)
$5*(a - 1) - 9*(a - 2) = - 3*(2a + 1) - 2$
$5*(-9-1) - 9*(-9-2) = - 3*[2*(-9)+1]-2$
$5*(-10) - 9*(-11) = - 3*[-18+1]-2$
$- 50 + 99 = - 3*[-17]-2$
$49 = 51-2$
$49 = 49\:(TRUE)$

Therefore: a = - 9