Francis+And+Jelson

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a number to a power means to multiply that number by itself as many times as indicated by the power, or exponent. This is the exponential value of the number which is much larger than simply multiplying the two numbers. 32 = (3)(3) = 9 vs. (3)(2) = 6

value- Absolute value can never be negative. Compute the problem as indicated inside the absolute value symbols. The result comes out of the absolute value signs as a positive. If there is a negative in front of the absolute value sign, the result would be a negative. |-5 - 4| = |-9| = 9 -|-5 - 4| = -|-9| = -9  A in front of a set of parentheses changes all signs inside the parenthesis and then disappears. It can be thought of as the distribution of a negative one (-1). -(m - 4) = -1(m - 4) = -1(m) - (-1)(4) = -m + 4

Adding like signs: When adding numbers with only positive signs, add the numbers (number of gains) and the answer is positive. When adding numbers with only negative signs, add the numbers (number of losses) and the answer is negative. -4 + (-8) = -12 Adding unlike signs: When adding numbers with unlike signs, subtract the lower number from the higher number and use the sign of the higher number. (Please note "higher" and "lower" refer to the absolute values of each number.) -5 + 7 = 2 5 + -7 = -2  Multiplying and Dividing like signs: Count the number of negative signs in the problem. If the number of negative signs is "even," the answer is positive. If the number of negative signs is "odd," the answer is negative. of Operations: 1. Complete all operations inside parentheses 2. Simplify any expressions using exponential notation. 3. Complete all multiplication and division in order from left to right. 4. Complete all addition and subtraction in order from left to right. Many folks use the mnemonic device: "//Please Excuse My Dear Aunt Sally//" to help them remember those steps. Please: ' P ' for parentheses Excuse: ' E ' for exponents My and Dear: ' M ' and ' D ' for multiplication and division Aunt and Sally: ' A ' and ' S ' for addition and subtraction CAUTION!! In word problems, "and" doesn't always mean to add. The operation word before the "and" indicates which operation sign to insert in place of the "and." A **linear equation** in one variable has a single unknown quantity called a **variable** represented by a letter. Eg: ‘//x//’, where ‘//x//’ is always to the power of 1. This means there is no ‘ //x//² ’ or ‘ //x//³ ’ in the equation. An equation is a statement that two quantities are equivalent. For example, this linear equation: // x // + 1 = 4 means that when we add 1 to the unknown value, ‘//x//’, the answer is equal to 4. To solve linear equations, you add, subtract, multiply and divide both sides of the equation by numbers and variables, so that you end up with a single variable on one side and a single number on the other side. As long as you always do the same thing to BOTH sides of the equation, and do the operations in the correct order, you will get to the solution. //For this example, we only need to subtract 1 from both sides of the equation in order to isolate 'x' and solve the equation:// // x // + 1 - 1 = 4 - 1 Now simplifying both sides we have: // x // + 0 = 3 So: // x // = 3 ||  With some practice you will easily recognise what operations are required to solve an equation. Here are possible ways of solving a variety of linear equation types. // x // + 1 = - 3 1. Subtract 1 from both sides: // x // + 1 - 1 = - 3 - 1 2. Simplify both sides: // x // =  - 4 - 2//x// = 12 1. Divide both sides by -2: 2. Simplify both sides: // x // =  - 6 1. Multiply both sides by 3: 2. Simplify both sides: x = - 6 2//x// + 1 = - 17 1. Subtract 1 from both sides: 2//x// + 1 - 1 = - 17 - 1 2. Simplify both sides: 2//x// = - 18 3. Divide both sides by 2: 4. Simplify both sides: x = - 9 1. Multiply both sides by 9: 2. Simplify both sides: 3//x// = 36 3. Divide both sides by 3: 4. Simplify both sides: x = 12 1. Multiply both sides by 3: 2. Simplify both sides: //x// + 1 = 21 3. Subtract 1 from both sides: //x// + 1 - 1 = 21 - 1 4. Simplify both sides: x = 20 7(//x// - 1) = 21 1. Divide both sides by 7: 2. Simplify both sides: x - 1 = 3 3. Add 1 to both sides: x - 1 + 1 = 3 + 1 4. Simplify both sides: x = 4 1. Multiply both sides by 5: 2. Simplify both sides: 3(//x// - 1) = 30 3. Divide both sides by 3: 4. Simplify both sides: x - 1 = 10 5. Add 1 to both sides: x - 1 + 1 = 10 + 1 6. Simplify both sides: //x // = 11 5//x// + 2 = 2//x// + 17 1. Subtract 2//x// from both sides: 5//x// + 2 - 2//x// = 2//x// + 17 - 2//x// 2. Simplify both sides: 3//x// + 2 = 17 3. Subtract 2 from both sides: 3//x// + 2 - 2 = 17 - 2 4. Simplify both sides: 3//x// = 15 5. Divide both sides by 3: 6. Simplify both sides: x = 5 5(//x// - 4) = 3//x// + 2 1. Expand brackets: 5//x// - 20 = 3//x// + 2 2. Subtract 3//x// from both sides: 5//x// - 20 - 3//x// = 3//x// + 2 - 3//x// 3. Simplify both sides: 2//x// - 20 = 2 4. Add 20 to both sides: 2//x// - 20 + 20 = 2 + 20 5. Simplify both sides: 2//x// = 22 6. Divide both sides by 2: 7. Simplify both sides: //x // = 11
 * The sum of a number and two. "Sum" means to add; therefore, replace the "and" with a plus sign (number plus two or "n + 2").
 * The difference of a number and two. "Difference" means to subtract; therefore, replace the "and" with a minus sign (number minus two or "n -2").
 * The product of a number and two. "Product" means to multiply; therefore, replace the "and" with a multiplication sign (number times two or "n * 2").
 * The quotient of a number and two. "Quotient" means to divide; therefore, replace the "and" with a division sign (number divided by two or "n/2").
 * The process of finding out the variable value that makes the equation true is called ‘solving’ the equation.**
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 * Example 1, Solve for ‘//x//’ :**
 * Example 2, Solve for ‘//x//’ :**
 * Example 3, Solve for ‘//x//’ :**
 * Example 4, Solve for ‘//x//’ :**
 * Example 5, Solve for ‘//x//’ :**
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 * Example 8, Solve for ‘//x//’ :**
 * Example 9, Solve for ‘//x//’ :**
 * Example 10, Solve for ‘//x//’ :**