What is the solution to –4|–2x + 6| = –24? a. x = 0 b. x = 0 or x = –6 c. x = 0 or x = 6 d. no solution

Answer: C. x = 0 or x = 6

Explanation/Steps:

-4|-2x+6|=-24 ← Divide both sides by -4

|-2x+6|=6

Then we use the rule where |f(x)| = a ⇒ f(x)=-a or f(x) = a

-2x+6 = -6 or -2x+6 = 6

First way:

-2x+6 = -6 ← Subtract 6 from both sides

-2x + 6 - 6 = -6 - 6

-2x = -12 ← Divide both sides by -2

x = 6

Second way:

-2x+6 = 6 ← Subtract 6 from both sides

-2x + 6 - 6 = 6 - 6

-2x = 0 ← Divide both sides by -2

x = 0

Answer: C. x = 0 or x = 6

Explanation/Steps:

-4|-2x+6|=-24 ← Divide both sides by -4

|-2x+6|=6

Then we use the rule where |f(x)| = a ⇒ f(x)=-a or f(x) = a

-2x+6 = -6 or -2x+6 = 6

First way:

-2x+6 = -6 ← Subtract 6 from both sides

-2x + 6 - 6 = -6 - 6

-2x = -12 ← Divide both sides by -2

x = 6

Second way:

-2x+6 = 6 ← Subtract 6 from both sides

-2x + 6 - 6 = 6 - 6

-2x = 0 ← Divide both sides by -2

x = 0

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1