Solve each equation for the variable. Show your work and check your solution. Steps to follow:

Step 1: Distribute First

Step 2: Combine like terms

Step 3: Solve the equation

1. 5x + 4x − 6x = 24 2. 8x + 5 − 4x + 1 = 46

3. 33 = 5(x + 8) + 3 4. 2x + 3(x − 8) = 1

5. x + x − 2x + 4x = −48 6. 2(x + 5) + 3x = 25

7. 60 = 4(x + 3) + 2(x − 3) 8. 47 = 2(x + 3) + 3(x − 3)

9. −2(x + 1.4) − 1.8 = 20.6 10. 8 − 2(x + 4) = 10

11. Tyler told his friend this riddle: “I am thinking of a number. Three times my number plus twice my number is twenty. What number am I thinking of?”

a) Write an equation that models Tyler’s statement.

b) Solve the equation. What number was Tyler thinking of?

1.  This is a like term

24 = 24

2. This is not a like term

12x - 6 = 46

3. This is not a like term

33 = 5x + 43

4.This is a like term

1 = 1

5. This is not a like term

7x = -48

6. This is a like term

25 = 25

7. This is a like term

60 = 60

8. This is a like term

47 = 47

9.This is a like term

20.6 = 20.6

10.This is a like term

10 = 10

Step-by-step explanation:

1. 5x + 4x − 6x = 24

5x + 4x = 9x

9x - 6x = 24

3x = 24

We can replace x and turn it into an 8.

3(8) = 24

3 x 8 = 24

24 = 24

This is a like term.

2. 8x + 5 − 4x + 1 = 46

8x + 4x - 5 + 1 = 46

8x + 4x = 12x

12x - 5 + 1 = 46

5 + 1 = 6

12x - 6 = 46

We cannot replace the x with any number to get 46.

So this is not a like term.

3. 33 = 5(x + 8) + 3

5xX= 5x

5 x 8 = 40

33 = 5x + 40 + 3

40 + 3 = 43

33 = 5x + 43

We cannot replace any number with x and get 33.

This is not a like term.

4. 2x + 3(x − 8) = 1

3 x X = 3x

3 x 8 = 24

2x + 3x - 24 = 1

2x + 3x = 5x

5x - 24 = 1

We can replace the x with 5.

5(5) - 24 = 1

5 x 5 = 25

25 - 24 = 1

1 = 1

This is a like term

5. x + x − 2x + 4x = −48

x + x = 1x because x is always a 1

1x - 2x +4x  = -48

1x + 2x = 3x

4x + 3x = 7x

7x = -48

We cannot replace x with any number.

This is not a like term.

6. 2(x + 5) + 3x = 25

2 x X = 2x

2 x 5 = 10

2x + 10 + 3x = 25

2x + 3x + 10 = 25

2x + 3x = 5x

5x + 10 = 25

We can replace the x with a 3.

5(3) + 10 = 25

5 x 3 = 15

15 + 10 = 25

25 = 25

This is a like term.

7. 60 = 4(x + 3) + 2(x − 3)

4 x X = 4x

4 x 3 = 12

60 = 4x + 12 + 2(x - 3)

2 x X = 2x

2 x 3 = 6

60 = 4x + 12 + 2x - 6

60 = 4x +2x +12 - 6

4x - 2x = 2x

60 = 2x + 12 - 6

12 - 6 = 6

60 = 2x + 6

We can replace the x with a 33.

60 = 2(33) - 6

2 x 33 = 66

66 - 6 = 60

60 = 60

This is a like term.

8. 47 = 2(x + 3) + 3(x − 3)

2 x X = 2x

2 x 3 = 6

47 = 2x + 6 + 3(x - 3)

3 x X = 3x

3 x 3 = 9

47 = 2x + 6 + 3x - 9

47 = 2x + 3x + 6 - 9

2x + 3x =  5x

47 = 5x + 6 - 9

6 - 9 = -3

47 = 5x + -3

We can replace the x with a 10.

47 = 5(10) + -3

5 x 10 = 50

47 = 50 + -3

50 + -3 = 47

47 = 47

This is a like term.

9. −2(x + 1.4) − 1.8 = 20.6

-2 x X = -2x

-2 x 1.4 = -2.8

-2x + -2.8 - 1.8 = 20.6

-2.8 - 1.8 = -4.6

-2x + -4.6 = 20.6

We can replace x with a 8.

-2(8) + -4.6 = 20.6

-2 x 8 = -16

-16 + -4.6 = 20.6

20.6 = 20.6

This is a like term.

10. 8 − 2(x + 4) = 10

2 x X = 2x

2 x 4 = 8

8 - 2x + 8 = 10

8 - 8 + 2x = 10

8 - 8 = 0

0 + 2x = 10

We can replace x with 5.

0 + 2(5) = 10

2 x 5 = 10

0 + 10 = 10

10 = 10

This is a like term.

I hope this helped. I am sorry if you get this wrong. Have a wonderful day.

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: