Solve for "x"
Miscellaneous
Simplify
Rules
Vocabulary
100
Solve: 2x + 2 = 18
x = 8
100

What letter is most commonly used to represent an unknown value or variable in algebra?

x

100

Simplify: 3(2d - 3) + d

Algebra: 7d - 9

100

What do you get if you raise any non-zero real number to the power of zero?

1

100

A letter (like x) that stands for an unknown number

Variable

200
Solve: 3x + 4 = 7
x = 1
200

What special name is given to the point (0,0) where the x-axis and y-axis intersect on a coordinate plane?

The origin

200

Simplify:

-6(6 + 5k) + 7(-k-5)

-71 - 37k

200

According to the order of operations, what must be evaluated before you perform addition or multiplication?

Parentheses

200

The number directly multiplied by a variable (like the 5 in 5x).

Coefficient

300

Solve: 21 = x - 17

x = 38

300

What is the traditional name for the rule used to expand the product of two binomials, which stands for First, Outer, Inner, Last?

FOIL method

Example

  • (4x + 6) (x + 3)

We look at the first binomials which are 4x and x which gives us 4x2

Now we look at the two outside binomials which are 4x and 3 which gives us 12x

Now we look at the two inside binomials which are 6 and x whichh gives us 6x

Now we look at the last two binomials which are 6 and 3 which gives us 18

Finally, you add all of them together to get: 4x2 +18x + 18

300
Simplify: a(b - c) - 2a(c + b)
-1ab - 3ac
300

Which property allows you to multiply the number outside the parentheses. Example: a(b + c) = ab + ac

The Distributive property

300

Must contain an equals sign (=); expressions do not.

Equation

400

Solve: 3x + 3 - 2x = 21

x = 18

400

What is the formula for slope intercept?

y = mx + b

In this formula, m represents the slope (the steepness of the line) and b represents the y-intercept (the point where the line crosses the y-axis).

 

400
Simplify: -4(3x - 2) -2(4 + 3x)
-18x
400

What property states that you can swap the order of numbers in an addition or multiplication problem without changing the final answer.  

 The Commutative Property

400

A plain number that stands alone and never changes value.

Constant

500

Solve: 4x - 5 - 3x + 2 - 2x = 9

x = -12

500

If we have a polynomial equation where the highest exponent is 2 (e.g., ax² + bx + c = 0), what specific name is given to this type of equation?

A quadratic equation

500

Simplify: 5(2x-3)-4(x-6)


The final simplified answer is (6x + 9).


Step-by-Step Solution

  1. Distribute the 5: Multiply (5) by both terms inside the first set of parentheses.
    This gives you: (10x - 15)
  2. Distribute the -4: Multiply (-4) by both terms inside the second set of parentheses. Remember that a negative times a negative equals a positive.
    This gives you: (-4x + 24)
  3. Combine the parts: Put the distributed terms together.
    (10x-15-4x+24)
  4. Group like terms: Combine the (x) terms together and the constant numbers together.
    • (x) terms: (10x - 4x = 6x)
    • Constants: (-15 + 24 = 9)
  5. Final Result: Combine them for the final expression.
    6x+9



500

This property states that you can regroup numbers in an addition or multiplication problem using parentheses without changing the final answer  (e.g., a + (b + c) = (a + b) + c)?

The Associative Property

500

A single number, a single variable, or numbers and variables multiplied together

Term

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