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Writing algebraic expressions or equations:
- Go word for word and underline key words. Write operations, variables and symbols above the words.
- Remember the key words to key operations: sum= add, product = multiply, difference = subtract and quotient = division.
- If the sentence has the word “THAN” in it, such as less than or more than, switch the order of those two terms. "More than, less than, Take it to the back!"
- Remember that “is” means equal sign.
Eleven less than twice a number is five more than number.
2n – 11 = n + 5
Simplifying expressions (no equal sign):
1.Use the distributive property if needed.
2. Combine like terms (terms with the same variable and the same exponent).
3. Watch the negative (subtraction) signs in front of your terms.
4. Use your integer rules!!!!
6(x – 2) + 4(x + 5)----distributive property
6x – 12 + 4x + 20----combine like terms
10x + 8
- Do the distributive property
- Then combine like terms on the same side of the equal sign. Cover up each side if needed.
- Move the variables to one side of the equal sign using the inverse operation (opposite).
- Then Solve: MOB story (Standard Method) or Tic Tac Toe
3(x + 5) = 2( x – 3) -----Distributive property
3x + 15 = 2x – 6 ----Move variables to same side using inverse ops.
1x + 15 = -6 ------Use inverse operations
x = -21
Evaluating Expressions- All variables should be replaced (substituted) by a number value:
- Rewrite the problem with the variables replaced with the numbers (substitute).
- Make sure you use parentheses to show multiplication problems.
- Rewrite the problem exactly like it is.
- Do the math by following the order of operations.
1st: (Parentheses), 2nd Exponents, 3rd: Multiply/Divide by working left to right, 4th: Add/Subtract by working left to right ------PEMDAS
Example: 3x2 + y if x =3 and y=-1
3(32) + (-1)
3(9) – 1
Solving for a specific variable:
- Circle the variable for which you are solving.
- Do the inverse operations to isolate the variable.
- Rewrite the new equation.
Example: m – 5 = n Example: V = lwh
m – 5 = n Solve for m. V = lwh Solve for h.
+ 5 +5 (Inverse) lw lw (Inverse)
m = n + 5 h = V
Solve inequality problems:
- If needed, solve just like an equation-Mob Story or TicTacToe.
- Graph on a number line.
- Check the inequality symbol to decide if you will use an open circle or closed circle. Open: <, > Closed: ≥, ≤
- Shade in the direction the direction the symbol is pointing if the variable is on the left side.
(Greater than to the right, Less than to the left)
- *** If multiplying or dividing by a negative, switch the direction of the inequality symbol.
Example: -2x + 5 ≥ 15 Solve for x.
-5 -5 Inverse
-2x ≥ 10
-2 -2 Dividing by a negative—Switch symbol
x ≤ -5 Graph:
-6 -5 -4
Solving absolute value equations:
1) Absolute values will always be equal to a positive value (distance from zero). l -3 l = 3 (which means 3 units from zero)
2) When solving for x, set up TWO equations-one for the positive value and one for the negative value.
3) First move any extras not inside the absolute value symbols.
4) Then set up the two equations and solve.
5) ***If what is inside the absolute value involves addition or subtraction, your two answers will be different numbers.
Extras? l x – 4 l + 10 = 14 l x l = 5
-10 -10 x = 5, x = -5
Set up 2 equations---- l x – 4 l = 4
x – 4 = 4 x – 4 = -4
+4 +4 +4 +4
x = 8 x = 0
Same signs, add and keep
Different signs, subtract
Take the sign of the larger number
Then it will be exact.
Multiplying and dividing Integers
Same signs –positive
Different signs- negatives