How Many Solutions? Quick Check 3 of 53 of 5 Items Question Justify why −12(x−3)−52=−16 has one solution, infinitely many solutions, or no solution.(1 point) Responses It has one solution, because the solution is in the form x=a . The solution is x=−12 . It has one solution, because the solution is in the form x equals a . The solution is x equals negative 12 . It has one solution because the solution is in the form x=a . The solution is x=0 . It has one solution because the solution is in the form x equals a . The solution is x equals 0 . It has infinitely many solutions because the solution is in the form a=a . It has infinitely many solutions because the solution is in the form a equals a . It has no solution because the solution is in the form a=b .
The correct response is "It has one solution, because the solution is in the form x=a. The solution is x=−12."
To solve the equation −12(x−3)−52=−16, we can start by simplifying the expression using the distributive property:
-12(x-3) - 5(2) = -16
-12x + 36 - 10 = -16 (rearranging the terms)
-12x + 26 = -16 (combining like terms)
-12x = -16 - 26 (subtracting 26 from both sides)
-12x = -42 (simplifying further)
Next, we can isolate x by dividing both sides of the equation by -12:
-12x / -12 = -42 / -12
x = 3.5
Therefore, the solution to the equation is x = 3.5, which means it has one solution.