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Simplifying expressions: 🟢

Distributive property: 🔴

Equations with variables on both sides: 🟣

Different step equations: 🟡

Special cases equations: 🔵

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Expression: A mathematical phrase that can contain numbers, variables, and operators.

Term: a constant or a variable in an expression. which are separated by + and - signs.

Coefficient: The number in front of a variable.

Like terms: numbers with the same base or variables and the same exponent.

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13(for example) is a number

15x, x is a variable

-3.5x+4a+12y= expression

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when simplifying expressions you have to combine like terms

exapmles:

1x + 19x - 3h + 6h

= 20x +3h

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when you do a one step equation you have to isolate the variable by using inverse, or opposite operation. one step equation is when you only need one step to solve an equation

example:

2x = 6

x = 3

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when you do two step equation you have to first add or subtract to remove constant. then you have to multiply or divide to remove coefficient.

example:

7m - 17 = 60. ( add 17 to 60)

7m = 77. ( divide by 7 to both sides)

m= 11

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Starts by subtracting or adding the coefficient depending on the number. Subtract if number is positive and add if negative. Subtract it by any coefficient. One coefficient should get cancelled from this.

Then add or substance the number (not the variable) from both sides.

This should end you up with a variable that equals to a number.

Example:

7n - 7 = 2n + 23

5n - 7 = 23

5n = 30

N = 6

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Equation with variables on both side examples

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Equation with variables on both side examples

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More Examples:

8x - 7 = 4x + 21

4x -7 = 21

4x = 28

X = 7

-11x + 9 = -2x + 45

-9x + 9 = 45

-9x = 36

X = -4

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If possible and/or necessary, combine like terms on the same side of the equation first. Then we'll isolate the variable to solve the equation.

E.g:

-14=7w+2w+8.5

-14=9w+8.5 (combining like terms)

-22.5=9w (divide -22.5 by 9)

w= -2.5 (isolate the variable to solve the equation)

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Multiplying each term outside the "(-)" by the number inside.

E.g: 2(3g-7) = 6g-14

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when simplifying expression with distributive property, you have ti multiply each term outside the parentheses by the number inside.

examples:

-8(4y + 5)

= -32y - 40

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In this topic includes:

One solution, no solution and all real numbers

One solution:

This means that there’s only 1 solution to the problem.

No solution:

Means that there’s no solution into solving the problem.

All real numbers:

That means the numbers are equal to each other. Like if it ends up with something like this : -13=-13

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One solution - Variable = number

Example:

2( ) = -10

No solution - LHS (left hand side) is not equal to RHS (right hand side)

Example:

( ) - 7 = ( ) + 7

Multiple solution - LHS (consant) = RHS (consant)

Example:

2 + ( ) = 2 + ( )