solve for x. (11 points)
4) x - 10 = 3
5) 4x + 6 = - 10
6) (\frac{x}{2}+4 = 12)
7) 10x = 2x - 30 + 3x
8) 12x - 6x+3(2x - 15)=21
9) 8x + 12 = 6x + 40
writing equations (points)
10) given a rectangle with an area of 68 sq. in. and a length of 17 in., find the width.
11) if the circumference of a circle, find the radius.
12) given a triangle with an area of 48 sq. in. and a height of 8 in., find its base.
13) given a triangle with a perimeter, side length of 18 m., and incomplete text, find the third missing side

Question

Accepted Answer

### 4. Solve for $x$ in $x - 10=3$
# Explanation:
## Step1: Add 10 to both sides
$$x- 10+10=3 + 10$$
## Step2: Simplify
$$x=13$$
# Answer:
$x = 13$

### 5. Solve for $x$ in $4x+6=-10$
# Explanation:
## Step1: Subtract 6 from both sides
$$4x+6 - 6=-10 - 6$$
$$4x=-16$$
## Step2: Divide both sides by 4
$$\frac{4x}{4}=\frac{-16}{4}$$
# Answer:
$x=-4$

### 7. Solve for $x$ in $10x = 2x-30 + 3x$
# Explanation:
## Step1: Combine like - terms on the right - hand side
$$10x=5x - 30$$
## Step2: Subtract $5x$ from both sides
$$10x-5x=5x - 30-5x$$
$$5x=-30$$
## Step3: Divide both sides by 5
$$\frac{5x}{5}=\frac{-30}{5}$$
# Answer:
$x=-6$

### 8. Solve for $x$ in $12x-6x + 3(2x-15)=21$
# Explanation:
## Step1: Expand the expression
$$12x-6x+6x-45 = 21$$
## Step2: Combine like - terms
$$12x-45=21$$
## Step3: Add 45 to both sides
$$12x-45 + 45=21 + 45$$
$$12x=66$$
## Step4: Divide both sides by 12
$$\frac{12x}{12}=\frac{66}{12}=\frac{11}{2}=5.5$$
# Answer:
$x = 5.5$

### 9. Solve for $x$ in $8x+12=6x + 40$
# Explanation:
## Step1: Subtract $6x$ from both sides
$$8x+12-6x=6x + 40-6x$$
$$2x+12=40$$
## Step2: Subtract 12 from both sides
$$2x+12-12=40-12$$
$$2x=28$$
## Step3: Divide both sides by 2
$$\frac{2x}{2}=\frac{28}{2}$$
# Answer:
$x = 14$

### 10. Given a rectangle with an area $A = 68$ square inches and length $l = 17$ inches, find the width $w$
# Explanation:
## Step1: Use the area formula $A=l\times w$
$$w=\frac{A}{l}$$
## Step2: Substitute $A = 68$ and $l = 17$
$$w=\frac{68}{17}=4$$
# Answer:
The width is 4 inches.

### 11. If the circumference $C$ of a circle is known, and the formula for the circumference of a circle is $C = 2\pi r$, find the radius $r$
# Explanation:
## Step1: Solve the formula $C = 2\pi r$ for $r$
$$r=\frac{C}{2\pi}$$
# Answer:
$r=\frac{C}{2\pi}$

### 12. Given a triangle with an area $A = 48$ square inches and height $h = 8$ inches, find the base $b$
# Explanation:
## Step1: Use the area formula for a triangle $A=\frac{1}{2}bh$
$$b=\frac{2A}{h}$$
## Step2: Substitute $A = 48$ and $h = 8$
$$b=\frac{2\times48}{8}=12$$
# Answer:
The base is 12 inches.

(Note: Problem 13 is incomplete in the image, so it cannot be solved.)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

4. Solve for \(x\) in \(x - 10=3\)

Step1: Add 10 to both sides

Step2: Simplify

Step1: Subtract 6 from both sides

Step2: Divide both sides by 4

Step1: Combine like - terms on the right - hand side

Step2: Subtract \(5x\) from both sides

Step3: Divide both sides by 5

Answer:

5. Solve for \(x\) in \(4x+6=-10\)