Question

a popular online shaving club charges a $12 per month fee plus $1.50 per safety razor you purchase. write an equation for the cost (y) based on the number of razors (x) you purchase.
circle the gcf of 30x and 12x²y³.
30x: 2·3·5·x
12x²y³: 2·2·3·x·x·y·y·y
what algebraic property is demonstrated in the equation below?
5(8x - 4) - 10 = 40x - 20 - 10
solve:
p + 7 - 5 = -10 - 3p

Explanation:

Step1: Define cost equation structure

The total cost is fixed fee plus variable cost.
$y = (\text{cost per razor})x + \text{fixed fee}$
$y = 1.50x + 12$

Step2: Find GCF of terms

Identify common prime factors:
Common factors: $2, 3, x$
$\text{GCF} = 2 \times 3 \times x = 6x$

Step3: Identify algebraic property

The left side uses $a(b-c)=ab-ac$ to expand $5(8x-4)$ to $40x-20$.
This matches the Distributive Property.

Step4: Simplify the equation

Combine constants on left side:
$p + (7-5) = -10 - 3p$
$p + 2 = -10 - 3p$

Step5: Isolate variable terms

Add $3p$ to both sides:
$p + 3p + 2 = -10$
$4p + 2 = -10$

Step6: Isolate the variable

Subtract 2 from both sides, then divide by 4:
$4p = -10 - 2$
$4p = -12$
$p = \frac{-12}{4} = -3$

Answer:

1. $y = 1.50x + 12$
2. $6x$
3. Distributive Property
4. $p = -3$