6. solve for (x: 9 = 2x+23)
7. (7x = 28)
8. a rectangles perimeter is 46 cm. its length is 5 cm more than its width. find the original dimensions.
9. (3(x - 3)+2(x + 5)=x + 7)
10. (5+1/5)
11. select two that have infinitely many solutions:
a. (2(x - 3)=2x - 6)
b. (3x + 2=3x - 2)
c. (4(x + 3)=4x+12)
d. (x/2=(x + 4)/2 + 2)
12. ((48 - 18)/(15 - 3))

Question

Accepted Answer

### 6. Solve for $x$: $9 = 2x+23$
# Explanation:
## Step1: Isolate the term with $x$
Subtract 23 from both sides.
$9 - 23=2x+23 - 23$
$- 14 = 2x$
## Step2: Solve for $x$
Divide both sides by 2.
$x=\frac{-14}{2}=-7$
# Answer:
$x = - 7$

### 7. $7x=28$
# Explanation:
## Step1: Solve for $x$
Divide both sides by 7.
$x=\frac{28}{7}=4$
# Answer:
$x = 4$

### 8. A rectangle's perimeter is 46 cm. Its length is 5 cm more than its width. Find the original dimensions.
Let the width of the rectangle be $w$ cm. Then the length $l=w + 5$ cm.
The perimeter formula for a rectangle is $P = 2(l + w)$.
# Explanation:
## Step1: Substitute into the perimeter formula
Substitute $P = 46$, $l=w + 5$ into $P=2(l + w)$.
$46=2((w + 5)+w)$
$46=2(2w + 5)$
## Step2: Expand the right - hand side
$46 = 4w+10$
## Step3: Isolate the term with $w$
Subtract 10 from both sides.
$46-10=4w+10 - 10$
$36 = 4w$
## Step4: Solve for $w$
Divide both sides by 4.
$w=\frac{36}{4}=9$
## Step5: Find the length
Since $l=w + 5$, then $l=9 + 5=14$
# Answer:
Width $w = 9$ cm, Length $l = 14$ cm

### 9. $3(x - 3)+2(x + 5)=x+7$
# Explanation:
## Step1: Expand the left - hand side
Use the distributive property $a(b + c)=ab+ac$.
$3x-9 + 2x+10=x + 7$
## Step2: Combine like terms on the left - hand side
$(3x+2x)+(-9 + 10)=x + 7$
$5x+1=x + 7$
## Step3: Isolate the terms with $x$ on one side
Subtract $x$ from both sides and subtract 1 from both sides.
$5x - x=7 - 1$
$4x=6$
## Step4: Solve for $x$
Divide both sides by 4.
$x=\frac{6}{4}=\frac{3}{2}$
# Answer:
$x=\frac{3}{2}$

### 10. $5+\frac{1}{5}$
# Explanation:
## Step1: Rewrite 5 as a fraction with a denominator of 5
$5=\frac{25}{5}$
## Step2: Add the fractions
$\frac{25}{5}+\frac{1}{5}=\frac{25 + 1}{5}=\frac{26}{5}=5\frac{1}{5}$
# Answer:
$\frac{26}{5}$ or $5\frac{1}{5}$

### 11. Select TWO that have infinitely many solutions.
a. $2(x - 3)=2x-6$
# Explanation:
## Step1: Expand the left - hand side
$2x-6=2x - 6$
This is an identity, so it has infinitely many solutions.
b. $3x + 2=3x-2$
# Explanation:
## Step1: Subtract $3x$ from both sides
$3x-3x + 2=3x-3x-2$
$2=-2$, which is a contradiction, so it has no solutions.
c. $4(x + 3)=4x+12$
# Explanation:
## Step1: Expand the left - hand side
$4x+12=4x + 12$
This is an identity, so it has infinitely many solutions.
d. $\frac{x}{2}=\frac{x + 4}{2}+2$
# Explanation:
## Step1: Multiply both sides by 2 to clear the fractions
$x=x + 4+4$
$x=x + 8$, subtract $x$ from both sides: $0 = 8$, which is a contradiction, so it has no solutions.
# Answer:
a. $2(x - 3)=2x-6$, c. $4(x + 3)=4x+12$

### 12. $\frac{48-18}{15 - 3}$
# Explanation:
## Step1: Calculate the numerator and denominator separately
The numerator $48-18 = 30$, the denominator $15 - 3=12$.
## Step2: Simplify the fraction
$\frac{30}{12}=\frac{5}{2}=2.5$
# Answer:
$\frac{5}{2}$ or $2.5$

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QUESTION IMAGE

Question

Explanation:

6. Solve for \(x\): \(9 = 2x+23\)

Step1: Isolate the term with \(x\)

Step2: Solve for \(x\)

Step1: Solve for \(x\)

Step1: Substitute into the perimeter formula

Step2: Expand the right - hand side

Step3: Isolate the term with \(w\)

Step4: Solve for \(w\)

Step5: Find the length

Answer:

7. \(7x=28\)