Solving equations for Y
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The document provides step-by-step instructions for solving equations for a variable by isolating it on one side of the equation. It demonstrates the process for a variety of equations, showing how to move all other terms to the other side by taking their opposite and then dividing both sides by the coefficient of the variable. The goal is to isolate the variable y on one side of the equation with any numbers or other variables on the other side.
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Inequalities ppt revised
Here are the steps to solve each inequality and graph the solution:
1) m + 14 < 4
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m < -10
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Graph: y < -6
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helping you to solve linear equation easily
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Fundamentals of Algebra
Chu v. Nguyen
Integral Exponents
Exponents
If n is a positive integer (a whole number, i.e., a number without decimal part) and x is a number, then
The number x is called the base and n is called the exponent.
The most common ways of referring to are “ x to the nth power,”
“ x to the nth,” or “the nth power of x.”
Integral Exponents (cont.)
For any non-zero number x and a positive integer n
and
Note: is not defined
and
Rules Concerning Integral Exponents
Following are five rules in which m and n are positive integers:
Rule 1: ; for example,
Rule 2: ; for example
or
Rules Concerning Integral Exponents (Cont.)
Rule 3: ; for example
or
Rule 4: ; for example
or
Rule 5: ; for example
or
Basic Rules for Operating with Fractions
Since dividing by zero is not defined, we assume that the denominator
is not zero.
Following are the eight basic rules for operating with fractions.
Rule 1: ; for example
Rule 2: ; for example
Rule 3: ; for example
Basic Rules for Operating with Fractions (cont.)
Rule 4: ; for example
Rule 5: ; for example
Rule 6: ; for example
Basic Rules for Operating with Fractions (cont.)
Rule 7: ; for example
Rule 8: ; for example
Notes: a*b +a*x may be expressed as a(b + x)
a*b + 1 may be written as a(b + ), and
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Square Root
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for
When n = 2, we say that x is the square root of “a” and is denoted by
or or
For example:
or
Practices
Carrying out the following operations:
24 ; 2-2 ; 2322, ; 252-5 ; and (2x3)5
; ; ; and
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Chapters Summary (X class)
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Solving equations for Y
- 1. Solving For Y Created by Mrs. Ulshafer March 14, 2010
- 2. Solve each equation for y y – 2x = 1 +2x + 2x y = 2x + 1 Leave the y (in red), move everything else Opposite of -2x is +2x Can't combine +2x & 1 (not like terms) Since the y is positive with no other numbers in front you are done.
- 3. Solve each equation for y 3x + y = 3 -3x -3x y = -3x + 3 Leave the y (in red), move everything else Opposite of 3x is -3x Can't combine -3x & 3 (not like terms) y is alone and positive, nothing left to do
- 4. Solve each equation for y 4x + 2y = 1 -4x -4x + 2y = -4x + 1 2 2 2 y = -2x + 1/2 Leave the y (in red), move everything else Opposite of +4x is -4x Can't combine -4x & 1 (not like terms) Opposite of 2 times y, is division Simplify as much as possible. (No decimals, leave as fractions)
- 6. Solve each equation for y 2x + 3y = 10 -2x -2x 3y = -2x + 10 /3 /3 /3 y = -2x/3 + 10/3 Leave the y (in red), move everything else Opposite of +2x is -2x Can't combine -2x & 10 (not like terms) Opposite of 3 times y, is divide Simplify as much as possible. (No decimals, leave as fractions)
- 7. Solve each equation for y 2y – 4x = 6 +4x +4x 2y = 4x + 6 /2 /2 /2 y = 2x + 3 Leave the y (in red), move everything else Opposite of -4x is +4x Can't combine 4x & 6 (not like terms) Opposite of 2 times y, is divide Simplify as much as possible. (No decimals, leave as fractions)
- 8. Solve each equation for y 6y – 3x = -9 + 3x +3x 6y = 3x – 9 /6 /6 /6 y = 1x/2 - 3/2 Leave the y (in red), move everything else Opposite of -3x is +3x Can't combine 3x & -9 (not like terms) Opposite of 6 times y, is division Simplify as much as possible. Reduce fractions (No decimals, leave as fractions)
- 9. Solve each equation for y -5x – 8y = 15 +5x +5x – 8y = 5x + 15 /-8 /-8 /-8 y = -5x/8 - 15/8 Leave the y (in red), move everything else Opposite of -5x is +5x Can't combine 5x & 15 (not like terms) Opposite of -8 times y, is divide Negative / positive = negative (No decimals, leave as fractions)
- 10. Solve each equation for y 2x – y = 7 -2x -2x -y = -2x + 7 /-1 /-1 /-1 y = 2x - 7 Leave the y (in red), move everything else Opposite of 2x is -2x Can't combine -2x & 7 (not like terms) divide both sides by negative 1 to make y positive Negative / negative = positive (2x) Positive / negative = negative (-7)
- 11. Solve each equation for y -2x – 3y = -6 +2x +2x -3y = 2x – 6 /-3 /-3 /-3 y = -2x/3 + 2 Leave the y (in red), move everything else Opposite of -2x is 2x Can't combine 2x & 7 (not like terms) Opposite of -3 times y, is division positive / negative =negative negative / negative =positive (+2) Divide or reduce fractions, no decimals.