Algebra is fun!
x + 3 = 7
1. Subtract the constant term from both sides of the equation to isolate the variable term.
x = 7 - 3
x = 4
x - 2 = 10
1. Add 2 to both sides of the equation to isolate the variable term.
x = 12
y/2 = 10
1. Multiply both sides by 2 to eliminate the fraction on the left side.
y = 20
10y = 100
1. Divide both sides of the equation by 10 to isolate the variable y.
y = 10
What is the inverse for ALL the operations?
Addition: The inverse operation of addition is subtraction.
Subtraction: The inverse operation of subtraction is addition.
Multiplication: The inverse operation of multiplication is division.
Division: The inverse operation of division is multiplication.
2x - 5 = 15
1. Add 5 to both sides of the equation to isolate the variable term.
2x = 20
2. Divide both sides by 2 to find the value of x.
x = 10
3x + 2 = 10
1. Subtract 2 from both sides of the equation to isolate the variable term.
3x = 8
2. Divide both sides by 3 to find the value of x.
x = 8/3
4y - 2 = 22
1. Add 2 to both sides of the equation to isolate the variable term.
4y = 24
2. Divide both sides by 4 to find the value of y.
y = 6
6w + 2 = 22
1. Subtract 2 from both sides of the equation to isolate the variable term.
6w = 20
2. Divide both sides by 6 to find the value of w.
w = 20/6
Finish the sentence!!
When solving algebraic equations, what you do to one side __________________.
YOU MUST DO TO THE OTHER!
2x - 5 = -10
1. Add 5 to both sides of the equation to isolate the variable term.
2x = -5
2. Divide both sides by 2 to find the value of x.
x = -5/2
5y - 10 = 2
1. Add 10 to both sides of the equation to isolate the variable term.
5y = 12
2. Divide both sides by 5 to find the value of y.
y = 12/5
8x + 2 = 58
1. Subtract 2 from both sides of the equation to isolate the variable term.
8x = 56
2. Divide both sides by 8 to find the value of x.
x = 7.
3w - 10 = -2
1. Add 10 to both sides of the equation to isolate the variable term.
3w = 8
2. Divide both sides by 3 to find the value of w.
w = 8/3
What are the integer rules for multiplication and division?
Same signs = positive number
Different signs = negative number
2(x + 1)= -12
1. Distribute the 2 through the parentheses.
2x + 2 = -12
2. Subtract 2 from both sides of the equation to isolate the variable term.
2x = -14
3. Divide both sides by 2 to find the value of x.
x = -7
2(y - 2) = -8
1. Distribute the 2 on the left side by multiplying it by both terms inside the parentheses.
2y - 4 = -8
2. Add 4 to both sides of the equation to isolate the variable term.
2y = -4
3. Divide both sides by 2 to find the value of y.
y = -2
2(x - 7) = -10
1. Distribute 2 to the terms inside the parenthesis.
2x - 14 = -10
2. Add 14 to both sides of the equation to isolate the variable term.
2x = 4
3. Divide both sides by 2 to find the value of x.
x = 2
3 (w - 2) = -12
1. First simplify the expression inside the parentheses by distributing the 3.
3w - 6 = -12
2. Add 6 to both sides of the equation to isolate the variable term.
3w = -6
3. Divide both sides by 3 to find the value of w.
w = -2
What is the difference between an algebraic EXPRESSION and an algebraic EQUATION?
Algebraic Expression- has no equal sign
Algebraic Equation- has an equal sign
-4(-3x - 1)= -2
1. Multiply -4 by each term inside the parentheses.
12x + 4 = -2
2. Subtract 4 from both sides of the equation to isolate the variable term.
12x = -6
3. Divide both sides by 12 to find the value of x.
x = -6/12
-3(-2x - 2)= -6
1. Distribute the -3 on the left side by multiplying it by both terms inside the parentheses.
6x + 6 = -6
2. Subtract 6 from both sides of the equation to isolate the variable term.
6x = -12
3. Divide both sides by 6 to find the value of x.
x = -2
-4(-3x - 9)= -12
1. Distribute -4 to the terms inside the parenthesis.
12x + 36 = -12
2. Subtract 36 from both sides of the equation to isolate the variable term.
12x = -48
3. Divide both sides by 12 to find the value of x.
x = -4
-2(-3x - 2) = -10
1. First simplify the expression inside the parentheses by distributing the negative sign.
6x + 4 = -10
2. Subtract 4 from both sides of the equation to isolate the variable term.
6x = -14
3. Divide both sides by 6 to find the value of x.
x = -14/6
Challenge question:
Sara solved her algebra question and she got -x=10. But her question asks for a positive x.
If -x=10 then what is +x or x equal to? How do you know?
-x=10 is the same as x=-10. You can multiply both sides by -1 to move the negative from one side to the other!