Answer:
73t + 15 & -16y - 2 // 3 & 4 // x = 45.65 & n = -1 & x ≤ -6
Step-by-step explanation:
Part 1:
13t(2+4)-5t + 15
use the distributive property and multiply your variable through the parentheses
( (13t x 2) + (13t x 4) ) -5t + 15
multiply the coefficient through
(26t + 52t) -5t +15
add the like terms within the parentheses first
78t - 5t + 15
add like terms as a whole since parentheses is done and simplify
73t + 15
-2(3y + 5) -2
apply the distributive property and multiply the coefficient
( (-2 x 3y) + (-2 x 5) ) -2
multiply through and add terms within parentheses
(-6y - 10y) -2
add like terms together within parentheses and then simplify the final expression
-16y - 2
Part 2:
apply the distributive property and solve normally each equation and see if the value of x given is true or plug in the x value that they give you and see when plugged in if the output is the same as the one shown
3. is true
plug in technique
8(1 + 5) = 48 (add like terms)
8(6) = 48 (multiply)
48 = 48 (check)
4. is true
plug in technique
2(-5) + 5 = -5 (multiply given value of x with coefficient)
-10 + 5 = -5 (add like terms and simplify)
-5 = -5 (check to see if true)
Part 3:
for all 3 equations, follow the order of operations or PEMDAS and simplify and combine like terms and solve for the given variable
a) x - 23.25 = 22.4 (add 23.25 to the other side and same side to get x alone)
x = 45.65
b) 23 - 3n = 26 (subtract 23 to get 3n alone from 26)
-3n = 3 (divide by -3 to get n alone from 3 --> 3/-3)
n = -1
c) -2 -5x ≥ 28 (add positive 2 to the other side of the inequality sign to get -5x alone)
-5x ≥ 30 (divide by -5 but since you are dividing by a negative you have to flip the sign)
x ≤ -6
