Algebra Bootcamp

Algebra Bootcamp

February 7, 2022​

Variables, Coefficients & Constants

• A variable is a letter that represents an unknown value

• A coefficient is a number directly in front of a variable. It is being multiplied by the variable.

• A constant is a number that is not connected to any variables.

Poll

Which is the constant? 5x + 4

• 5

• x

• 4

Poll

Which is the variable? 6k - 8

• 6

• k

• 8

Poll

Which is the coefficient? 7r + 12

• 7

• r

• 12

Multiple Select

Select all like terms with  $$6y$$  

• $$-2y$$  

• $$5y^2$$  

• 6

• $$\frac{1}{2}y$$  

• $$-12x$$  

Multiple Select

Select all the like terms with -11

• 2x

• 11

• 23

• 11y

• 99

Multiple Choice

Combine like terms
3x + 2x + 3y - 7y

• 5x + 10y
• 5x + 4y
• 5x - 4y
• 5x -10y

Multiple Choice

Simplify the expression: 7v + 2 + 12 + 2v

• 23
• 23v
• 9 + 14v
• 9v + 14

Multiple Choice

Simplify by combining like terms:
5a + 2b - 3a + 4

• 8a + 2b + 4
• 2a + 2b + 4
• 8ab
• 4ab + 4

To solve an equation you have to set out to meet one very important goal.

The variable(letter) has to be by itself on one side of the = sign and all the constants(numbers) should be on the other side

Equations must maintain balance or they fall apart.

if we do an operation to one side of the equal sign, we must do the same operation to the other side.

The original problem is 5 + x = 3

we need that 5 to goto the other side.

The opposite operator of + 5 is - 5.

Notice how when we subtract -5 from both sides, 5-5 on the left becomes 0. this achieves our goal of getting x by itself.

notice it says, m divided by 4 on the left side, to get m by itself we use the opposite operator. multiply is the opposite of division. if we multiply both sides by 4 that will get the m by itself on the left. 

Multiple Choice

What will you do to solve this equation?

X + 6 = 3

• subtract 6 from both sides

• add 6 to both sides

• subtract 3 from both sides

• add 3 to both sides

Multiple Choice

What will you do to solve this equation?

4x = 16

• divide both sides by 4

• multiply both sides by 4

• subtract 4 from both sides

• divide both sides by 16

Fill in the Blanks

Solve for x:

$-5x+7=152$   x=?

Fill in the Blanks

Solve for x:

$18x-10-17x+12=-4$ x=?

Fill in the Blanks

Solve for x:

$2x+8=3x-4$   x=?

Multiple Choice

Solve for x:

2x - 3 + 4x = 27

• x = 12

• x = 4

• x = 5

• x = 15

Multiple Choice

Solve for x: 
4x + 1 = 7x - 5

• -1
• 2
• 6/11
• 8

Fill in the Blanks

Solve for x:

$-2x-12=3x+3$