What does this equal? 6(x+1)+5=13-2+6x

1 answer:

7 0

<span>Simplifying 6(x + 1) + 5 = 13 + -2 + 6x Reorder the terms: 6(1 + x) + 5 = 13 + -2 + 6x (1 * 6 + x * 6) + 5 = 13 + -2 + 6x (6 + 6x) + 5 = 13 + -2 + 6x Reorder the terms: 6 + 5 + 6x = 13 + -2 + 6x Combine like terms: 6 + 5 = 11 11 + 6x = 13 + -2 + 6x Combine like terms: 13 + -2 = 11 11 + 6x = 11 + 6x Add '-11' to each side of the equation. 11 + -11 + 6x = 11 + -11 + 6x Combine like terms: 11 + -11 = 0 0 + 6x = 11 + -11 + 6x 6x = 11 + -11 + 6x Combine like terms: 11 + -11 = 0 6x = 0 + 6x 6x = 6x Add '-6x' to each side of the equation. 6x + -6x = 6x + -6x Combine like terms: 6x + -6x = 0 0 = 6x + -6x Combine like terms: 6x + -6x = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.</span>

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Determine 2nd term and rth term of a.p.whose 6 th term is 12 and 8 th term is 22

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Answer: $\bold{a_2=-8\qquad \qquad a_r=5r-18}$

<u>Step-by-step explanation:</u>

Given: a₆ = 12 a₈ = 22

$d=\dfrac{a_8-a_6}{8-6}\quad = \dfrac{22-12}{8-6}\quad =\dfrac{10}{5}\quad =\boxed{5}$

$a_n=a_0+d(n-1)\\\\\\\underline{\text{Use}\ a_6\ \text{to find}\ a_o}\\a_6=a_o+5(6-1)\\\\12=a_o+5(6-1)\\\\12=a_o+25\\\\a_0=\boxed{-13}\\\\\\\underline{\text{Equation:}}\\a_n=13+5(n-1)\\.\quad =-13+5n-5\\.\quad =5n-18\\\\\\\underline{2^{nd\ term:}}\\a_2=5(2)-18\\.\quad = 10-18\\.\quad =\boxed{-8}\\\\\\\underline{r^{th}\ term:}\\\boxed{a_r=5r-18}$