Question

answer
the correct answers are:
question 11: - 10
question 12: 4x - 8
question 13: 6
question 14: 3
question 15: 3, - 2
question 16: 5, - 5
question 17: ±11
question 18: ±5
explanation
here are the solutions to the math problems:

1. solve (2x = 6x + 40)

1 subtract (6x) from both sides
(2x-6x = 6x + 40-6x)
(-4x = 40)
2 divide both sides by (-4)
(\frac{-4x}{-4}=\frac{40}{-4})
(x=-10)

1. solve (4(x - 2)=)? (the problem is incomplete. ill assume it is meant to simplify the expression)

1 distribute the 4
(4(x - 2)=4cdot x-4cdot2)
(=4x - 8)

1. solve (\frac{7}{x + 8}=\frac{3}{x})

1 cross - multiply
(7cdot x=3cdot(x + 8))
(7x = 3x + 24)
2 subtract (3x) from both sides
(7x-3x = 3x + 24-3x)
(4x = 24)
3 divide both sides by 4
(\frac{4x}{4}=\frac{24}{4})
(x = 6)

1. solve (\frac{6}{x + 7}=\frac{3}{x + 2})

1 cross - multiply
(6cdot(x + 2)=3cdot(x + 7))
(6x + 12 = 3x + 21)
2 subtract (3x) from both sides
(6x + 12-3x = 3x + 21-3x)
(3x + 12 = 21)
3 subtract 12 from both sides
(3x + 12-12 = 21-12)
(3x = 9)
4 divide both sides by 3
(\frac{3x}{3}=\frac{9}{3})
(x = 3)

1. solve (|8x - 4| = 20)

1 set up two equations
(8x-4 = 20) or (8x - 4=-20)
2 solve the first equation
(8x-4 = 20)
(8x = 24)
(x = 3)
3 solve the second equation
(8x-4=-20)
(8x=-16)
(x=-2)

1. solve (|3x| = 15)

1 set up two equations
(3x = 15) or (3x=-15)
2 solve the first equation
(3x = 15)
(x = 5)
3 solve the second equation
(3x=-15)
(x=-5)

1. solve (x^{2}=121)

1 take the square root of both sides
(sqrt{x^{2}}=sqrt{121})
(x=pm11)

1. solve (x^{2}-7 = 18)

1 add 7 to both sides
(x^{2}-7 + 7 = 18 + 7)
(x^{2}=25)
2 take the square root of both sides
(sqrt{x^{2}}=sqrt{25})
(x=pm5)

Explanation:

Question 11

Step1: Subtract 6x from both sides

$$2x - 6x=6x + 40-6x$$
$$-4x = 40$$

Step2: Divide both sides by -4

$$\frac{-4x}{-4}=\frac{40}{-4}$$
$$x=-10$$

Question 12

Step1: Distribute the 4

$$4(x - 2)=4\cdot x-4\cdot2$$
$$=4x - 8$$

Question 13

Step1: Cross - multiply

$$7\cdot x=3\cdot(x + 8)$$
$$7x=3x + 24$$

Step2: Subtract 3x from both sides

$$7x-3x=3x + 24-3x$$
$$4x=24$$

Step3: Divide both sides by 4

$$\frac{4x}{4}=\frac{24}{4}$$
$$x = 6$$

Question 14

Step1: Cross - multiply

$$6\cdot(x + 2)=3\cdot(x + 7)$$
$$6x+12=3x + 21$$

Step2: Subtract 3x from both sides

$$6x+12-3x=3x + 21-3x$$
$$3x+12=21$$

Step3: Subtract 12 from both sides

$$3x+12-12=21-12$$
$$3x=9$$

Step4: Divide both sides by 3

$$\frac{3x}{3}=\frac{9}{3}$$
$$x = 3$$

Question 15

Step1: Set up two equations

$$8x-4 = 20\quad\text{or}\quad8x-4=-20$$

Step2: Solve the first equation

$$8x-4 = 20$$
$$8x=24$$
$$x = 3$$

Step3: Solve the second equation

$$8x-4=-20$$
$$8x=-16$$
$$x=-2$$

Question 16

Step1: Set up two equations

$$3x = 15\quad\text{or}\quad3x=-15$$

Step2: Solve the first equation

$$3x = 15$$
$$x = 5$$

Step3: Solve the second equation

$$3x=-15$$
$$x=-5$$

Question 17

Step1: Take the square root of both sides

$$\sqrt{x^{2}}=\sqrt{121}$$
$$x=\pm11$$

Question 18

Step1: Add 7 to both sides

$$x^{2}-7 + 7=18 + 7$$
$$x^{2}=25$$

Step2: Take the square root of both sides

$$\sqrt{x^{2}}=\sqrt{25}$$
$$x=\pm5$$

Answer:

Question 11: -10
Question 12: 4x - 8
Question 13: 6
Question 14: 3
Question 15: 3, -2
Question 16: 5, -5
Question 17: ±11
Question 18: ±5