Part I – Simplifying Expressions Simplify the following expressions:

13t (2+4)−5t + 15

-2 (3y + 5) – 2

Part II– Evaluating Expressions/Equations

True or False?

Each question below shows an equation and a value for x. Which of the following are true?

1. If 2(x−3)=−10 , then x=2.

2.
If 6x−2=20 , then x=− 3.

3. If 8(x+5)=48 , then x=1.

4.
If 2x+5=−5, then x=−5.

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Part III – Solving Equations and Inequalities

Solve the equation x – 23.25 = 22.4

Solve 23 - 3n = 26.

Solve −2 − 5x ≥ 28

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