in exercises 1 - 6, solve the equation.
1. $\frac{w - 10}{6}=15$
2. $4=\frac{1}{3}r - 6$
3. $1.4b - 11.2 = 2.8$
4. $4h-\frac{1}{9}=\frac{8}{9}$
5. $20 = 5(q - 11)$
6. $-8(11 + c)=0$
7. a rectangle has a perimeter of 446 feet. the rectangle has a length of $(13x - 1)$ feet and a width of $(9x + 4)$ feet. find the length and width of the rectangle.
8. the senior class orders a total of 256 class rings. the number of gold rings is 3 times the number of silver rings. how many gold rings and silver rings did the class order?

Question

Accepted Answer

### 1. Solve $\frac{w - 10}{6}=15$
# Explanation:
## Step1: Multiply both sides by 6
$w - 10=15	imes6$
$w - 10 = 90$
## Step2: Add 10 to both sides
$w=90 + 10$
$w = 100$
# Answer:
$w = 100$

### 2. Solve $4=\frac{1}{3}r-6$
# Explanation:
## Step1: Add 6 to both sides
$4+6=\frac{1}{3}r$
$10=\frac{1}{3}r$
## Step2: Multiply both sides by 3
$r=10	imes3$
$r = 30$
# Answer:
$r = 30$

### 3. Solve $1.4b-11.2 = 2.8$
# Explanation:
## Step1: Add 11.2 to both sides
$1.4b=2.8 + 11.2$
$1.4b=14$
## Step2: Divide both sides by 1.4
$b=\frac{14}{1.4}$
$b = 10$
# Answer:
$b = 10$

### 4. Solve $4h-\frac{1}{9}=\frac{8}{9}$
# Explanation:
## Step1: Add $\frac{1}{9}$ to both sides
$4h=\frac{8}{9}+\frac{1}{9}$
$4h = 1$
## Step2: Divide both sides by 4
$h=\frac{1}{4}$
# Answer:
$h=\frac{1}{4}$

### 5. Solve $20 = 5(q - 11)$
# Explanation:
## Step1: Divide both sides by 5
$\frac{20}{5}=q - 11$
$4=q - 11$
## Step2: Add 11 to both sides
$q=4 + 11$
$q = 15$
# Answer:
$q = 15$

### 6. Solve $-8(11 + c)=0$
# Explanation:
## Step1: Divide both sides by - 8
$11 + c=0\div(-8)$
$11 + c = 0$
## Step2: Subtract 11 from both sides
$c=0 - 11$
$c=-11$
# Answer:
$c=-11$

### 7.
The perimeter formula for a rectangle is $P = 2l+2w$. Given $P = 446$, $l=(13x - 1)$ and $w=(9x + 4)$.
# Explanation:
## Step1: Substitute into the perimeter formula
$446=2(13x - 1)+2(9x + 4)$
$446 = 26x-2 + 18x+8$
$446=44x + 6$
## Step2: Subtract 6 from both sides
$446-6=44x$
$440 = 44x$
## Step3: Divide both sides by 44
$x=\frac{440}{44}$
$x = 10$
## Step4: Find the length
$l=13x-1=13	imes10 - 1=129$
## Step5: Find the width
$w=9x + 4=9	imes10+4=94$
# Answer:
Length: 129 feet, Width: 94 feet

### 8.
Let the number of silver rings be $x$. Then the number of gold rings is $3x$.
# Explanation:
## Step1: Set up the equation
$x + 3x=256$
$4x=256$
## Step2: Divide both sides by 4
$x=\frac{256}{4}$
$x = 64$
## Step3: Find the number of gold rings
Number of gold rings $=3x=3	imes64 = 192$
# Answer:
Gold rings: 192, Silver rings: 64

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QUESTION IMAGE

Question

Explanation:

1. Solve $\frac{w - 10}{6}=15$

Step1: Multiply both sides by 6

Step2: Add 10 to both sides

Step1: Add 6 to both sides

Step2: Multiply both sides by 3

Step1: Add 11.2 to both sides

Step2: Divide both sides by 1.4

Answer:

2. Solve $4=\frac{1}{3}r-6$