If 2x - 3 = 4(x + 7) - 1, what is the value of 2x - 5?
First we need to solve the equation for "x". Step 1: Distribute 4(x+7), Step 2: Get the variable to one side of the equal sign by subtracting it (inverse operation). (2x - 4x - 3 = 4x - 4x + 28 - 1) Step 3: Add 3 to both sides of the equal sign (the inverse operation): -2x - 3 + 3 = 28 -1 + 3. Step 4: Combine all of the constants (like terms) on the right side of the equal sign: -2x = 30. Step 5: Divide both sides of the equal sign by -2 (the inverse operation- -2x means -2 times x): -2x/-2 = 30/-2. The result is x = -15. Substitute this value into 2x - 5 to get your answer. 2(-15) - 5 = -30 - 5 = -35. The answer is -35.
What is 3/4 - 1/2?
To be able to subtract these two fractions, you need equal parts. Think of a cookie broken up into 2 pieces and then one broken up into 4 pieces. You could not take an equal amount of pieces because they are not the same size. The denominator, or bottom number of the fraction tells you the size of the pieces, the top number, numerator, tells you how many of those pieces. To get the same size pieces, multiply the first fraction (1/2) by 2 on the top and bottom. Now you have 2/4 and 2 pieces of a cookie broken into 4 is the same amount as having 1 piece of a cookie broken up in 2 (1/2). Now you may subtract the number of pieces you need to. The new mathematical statement says 3/4 - 2/4. Subtract the number of pieces (the numerator) and keep the size of the pieces (denominator) the same: 3-2 = 1, therefore the answer is 1/4.
What is the difference between the an arithmetic and geometric sequence?
An arithmetic sequence is a Linear function that has a common difference, such as 2, 5, 8, 11,...where the common difference is +3 to get to the next term. An geometric sequence is an Exponential function that has a common ratio, or multiplier, such as 3, 6, 12, 24, 48,... which has a common multiplier of 2 each time. Geometric sequences grow faster that arithmetic sequences because it is multiplying. An example of an arithmetic sequence is saving $10 each month vs. a geometric sequence which would be having an interest rate of 2% on your savings account.