Transcript Unit 2
ALGEBRA Algebra is math that uses variables (letters) to represent an unknown quantity. VARIABLES Letters that stand in for unknown quantities. X, Y, D are commonly used, but any letter is ok. It’s your choice. COEFFICIENTS The number right next to a variable (no symbols in between). The indicated operation is multiplication. The coefficient tells you how many of that variable you have. Example, 9X means you have nine Xs 9X = X + X+X+X+X+X+X+X+X EXPRESSIONS Math phrases, they are not complete sentences because the are missing the “end punctuation” (an equal sign or inequality sign). Example: 4x + 2y – 6x Expressions can be simplified but not solved. EQUATIONS Math sentences. In algebra they contain variables. We can solve equations for our unknown quantity (our variable). Example: 3x = 18 LIKE TERMS Terms are parts of an expression or equation that are separated by + and – signs. Like terms are terms that have the same variable raised to the same power. Numbers with no variable (called a constant) are alike. Examples: x + 3x -2x are like terms. SIMPLIFYING EXPRESSIONS AND EQUATIONS To simplify and expression we combine like terms. That means that we add or subtract the terms that are alike (have the same variable raised to the same power). STEPS TO SIMPLIFYING 1. Identify like terms (circle, underline the matching terms). Make sure you include the sign in front so you know what to do in step two. 2. Combine like terms (add or subtract the matching terms that you identified). 3. Make sure that you have added/subtracted everything you can, there should be no matches left in your expression/equation. EXAMPLE Example: 3x + 4x – 2x + 5 – 2y Like terms: +3x, +4x and -2x Combine like terms: 3 + 4 – 2 = 5, that means I have a total of 5X in All. There are no remaining matches so my answer is: 5x + 5 – 2y SOLVING EQUATIONS This is the main thing that we do in Algebra!! We solve for unknowns. Step one, combine like terms if we can, if makes our work SIMPLER. SOLVING EQUATIONS CONT. We want to get our variable all by itself on one side of the equal sign, that is called isolating the variable. All of the numbers should be on the other side of the equal sign. SOLVING EQUATIONS CONT. To isolate the variable (clear out the numbers) we do the opposite (or inverse) operation of what we see. If we have more than one operation we should add or subtract before we multiply or divide. EXAMPLE FOR SOLVING EQUATIONS X + 6 = 10 What operation do we see? We see addition. What operation do we do? We do the opposite, which is to subtract. X + 6 = 10 We will subtract 6 from each side of the equation. X + 6 – 6 = 10 – 6 That leaves us with x = 4 NOW YOU TRY Remember to first identify the operation you see and then do the opposite. Y + 8 = 15 X–5=9 8 = x + 10 7=y-5 SOLVING EQUATIONS WITH MULTIPLICATION AND DIVISION 4X = 24 What operation do we see? We see multiplication. What operation do we do? We do the opposite, which is to divide. 4x = 24 We will divide both sides of the equation by 4. 4x = 24 4 So….1x = 6 4 4 = 1 4 and 24 = 6 4 NOW YOU TRY 5x = 30 4x = 12 22 = 6x - 32 = 8x EQUATIONS WITH DIVISION X = 4 7 What operation do we see? We see division. What operation do we do? We do the opposite, which is to multiply. X = 4 7 We will multiply both sides by 7. (7 ) x = 4 (7) 7 So……1x = 28 7 = 1 and 4(7) = 28 7 TWO STEP EQUATIONS Same procedures, just more steps. Add and subtract before you multiply and divide. 2X + 6 = 10 What operation do we see? We see addition. What operation do we do? We do the opposite, which is to subtract. 2X + 6 = 10 We will subtract 6 from each side of the equation. 2X + 6 – 6 = 10 – 6 Now we have 2X = 4 Are we done? Is X by itself yet? No. 2x = 10 Now what operation do we see? We see multiplication, so we do division 2x 2 = 10 2 x=5 Now you try: 3x – 5 = 10 2x - 6 = 8 Y+ 4 = 7 6