Solve the inequality -2 < 3x+1 < 13.
When solving inequalities, keep the following facts in mind: a < b if and only if ac < bc if c > 0 a < b if and only if ac > bc if c < 0 lal < b if and only if -b < a < b lal > b if and only if a < -b or a > b So let's start by looking at the inequality. -2 < 3x+1 < 13 If we do something to one part of the inequality we must to it to each part. With that said, let's subtract 1 from each term. -3 < 3x < 12 Now we can easily see that these terms are easily divisible by 3 so let's divide by 3. -1 < x < 4 Therefore the solution is (-1, 4)
Solve for t. -3t + 2 = 8
To solve for t you will want to get t all by itself on one side. (Remember: If you do something to one side of the equation, you must do it to the other side to keep the equation equal.) Let's start by subtracting the 2. -3t + 2 - 2 = 8 - 2 -3t = 6 Now we must divide -3t by -3 to get the t by itself. If we do that we must also divide 6 by -3 to even out the equation. -3t/-3 = 6/-3 t = -2
John's annual salary after a raise of 15% is $45,000. What was his salary before the raise?
We need to find out what John's salary was before he got his raise. So, x will represent his salary before the raise. Let's write down the values we now know, x = John's salary before his raise x(15%) = x(.15) = The amount of John's raise $45,000 = John's salary now Now we will put that into an equation that will help us to solve the problem. x + x(.15) = 45,000 Now we can solve for x. Add the x's together. (Remember: if you see no number with a variable, it means there is an invisible 1 there because 1 multiplied by any number is always the number itself.) 1.15x = 45,000 Now we divide both sides by 1.15 in order to get the x by itself. (Remember: dividing a number by itself will always equal 1. The only exception to that rule is the number 0.) 1.15x/1.15 = 45,000/1.15 x = 39,130