1.)A number decreased by 32 is -58. Find the number.

The number is ____. (Give only the value of the number as your answer.
2.)The product of 14 and n is -28. Write the algebraic equation
3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike?
4.)Alex is six years older than his sister, Emma. The sum of their ages is 32. How old is Alex?

Alex is ____ years old.
5.)Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52. How old is Mousy?

Mousy is ____ years old
6.)Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike?
7.)The sum of three consecutive integers is 108. Which equation would be used to solve this word problem? (HINT: The equation has been simplified some...)

3x + 3 = 108
3x = 108
3(x+3) = 108
3x + 1 = 108

1. x - 32 = -58

Solve for x.

2. 14n = -28

3. r = b + 14

r + b = 300

Substitute b+14 for e in second equation and solve for b. If you want, insert that value into the first equation and solve for r. Check by inserting both values into the second equation.

4-6. Use similar method to 3.

7. x + x+1 +x+2 = 108

Combine terms.

1.) The number is -26.

2.) The algebraic equation is 14n = -28.

3.) Let the price of the red bike be x. The equation would be x + (x - 14) = 300.

4.) Let Emma's age be x. Alex's age would be x + 6. The equation would be x + (x + 6) = 32.

5.) Let Mousy's age be x. Mrs. Computer's age would be 3x. The equation would be x + 3x = 52.

6.) Let Tom's age be x. Mike's age would be 2x + 5. The equation would be x + (2x + 5) = 65.

7.) The equation 3x + 3 = 108 would be used to solve this word problem.

1.) To find the number, we can set up an equation using the information given. Let's represent the number as "x". We are told that the number decreased by 32 is equal to -58, so we can write the equation as:

x - 32 = -58

To find the value of x, we can solve this equation. We add 32 to both sides of the equation to isolate x:

x - 32 + 32 = -58 + 32
x = -26

So the number is -26.

2.) Let's represent the unknown number as "n". We are told that the product of 14 and n is equal to -28. The word "product" indicates multiplication, so the algebraic equation can be written as:

14n = -28

To solve for n, we divide both sides of the equation by 14:

14n/14 = -28/14
n = -2

So the algebraic equation is 14n = -28 and the value of n is -2.

3.) Let's represent the price of the red bike as "x". We are told that the blue bike is $14 less than the red bike, so the price of the blue bike can be represented as "x - 14". The sum of their prices is $300, so we can write the equation:

x + (x - 14) = 300

To solve for x, we simplify the equation:

2x - 14 = 300

Then, we add 14 to both sides of the equation:

2x - 14 + 14 = 300 + 14
2x = 314

Finally, we divide both sides of the equation by 2:

2x/2 = 314/2
x = 157

So the price of the red bike is $157.

4.) Let's represent Emma's age as "x". We are told that Alex is six years older than Emma, so Alex's age can be represented as "x + 6". The sum of their ages is 32, so we can write the equation:

x + (x + 6) = 32

To solve for x, we simplify the equation:

2x + 6 = 32

Then, we subtract 6 from both sides of the equation:

2x + 6 - 6 = 32 - 6
2x = 26

Finally, we divide both sides of the equation by 2:

2x/2 = 26/2
x = 13

So Alex is 13 years old.

5.) Let's represent Mousy's age as "x". We are told that Mrs. Computer is 3 times older than Mousy, so her age can be represented as "3x". The sum of their ages is 52, so we can write the equation:

x + 3x = 52

To solve for x, we simplify the equation:

4x = 52

Then, we divide both sides of the equation by 4:

4x/4 = 52/4
x = 13

So Mousy is 13 years old.

6.) Let's represent Tom's age as "x". We are told that Mike is 5 years more than twice as old as Tom, so Mike's age can be represented as "2x + 5". The sum of their ages is 65, so we can write the equation:

x + (2x + 5) = 65

To solve for x, we simplify the equation:

3x + 5 = 65

Then, we subtract 5 from both sides of the equation:

3x + 5 - 5 = 65 - 5
3x = 60

Finally, we divide both sides of the equation by 3:

3x/3 = 60/3
x = 20

So Tom is 20 years old.

7.) The sum of three consecutive integers is 108. The key here is that the integers are consecutive, which means they follow each other in order without skipping any numbers. Let's represent the first consecutive integer as "x". The next two consecutive integers will be "x + 1" and "x + 2".

The equation that represents the sum of these three consecutive integers can be written as:

x + (x + 1) + (x + 2) = 108

Simplifying this equation, we get:

3x + 3 = 108

So the equation that would be used to solve this word problem is 3x + 3 = 108.