Question

1. Simplify the expression and show each step.

6x+1 -(3x-1

2. Which expression is equivalent to
(3x-1)-2.75(x+2

3. Matt and his friends paid $30 for 4 sandwiches and 4 bottles of water. Each sandwich cost the same amount. The bottles of water cost $2 each. how much does the sandwich cost

Answer 1

1. 3x + 2

2. 0.25x - 6.5

3. $5.50 per sandwich

Explanation:

1.

6x + 1 - (3x - 1)

PEMDAS says solve everything in the parentheses first

There is nothing left to simplify within the parentheses.

Since there's also no exponents, multiplication, or division, let's combine like terms starting from left to right

6x - 3x + 1 + 1

Negative + Negative = Positive, hence why it became 1 + 1

3x + 2

2.

(3x - 1) - 2.75 (x + 2)

PEMDAS says to do multiplication next (since parentheses are fully simplified and there are no exponents)

(3x - 1) - 2.75x - 5.5

Negative + Positive = Negative, hence why it became -5.5

3x - 1 - 2.75x - 5.5

Combine like terms

3x - 2.75x - 1 - 5.5

0.25x - 6.5

3.

Set up an equation:

Variable x = cost of sandwiches

4x + 4(2) = 30

4x + 8 = 30

Subtract 8 from both sides to isolate the variable

4x + 8 - 8 = 30 - 8

4x = 22

Divide both sides by 4

4x ÷ 4 = 22 ÷ 4

x = 5.5

$5.50 per sandwich