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There are a multitude of "rules" in math, algebra, calculus, and geometry. While nobody could possibly expect you to remember each and every one (unless, you know, it's your job), you ARE required to know the basics. . . such as the rule you will apply to these problems.

Remember this. . .when working with anything in Math, what you apply to one side of the equation must be replicated to the other side.

What is the equation, you say? The perfect examples are all four of the questions you're being asked!!!

Another rule you must remember. . .always, always, always work to isolate the variable when attempting to produce the variable's value.

What do I mean by this? When you have a problem such as x+7 = 12, you need to figure out what that variable ACTUALLY is to produce "12" by adding "7".

What is the variable, you ask?? The variable is "x", of course! Do note that variables DO come in all shapes, sizes, and forms, so your variable might not always be "x." In fact, it can be any of the letters in the alphabet. Luckily, you won't have to worry about that. . .yet.

And perhaps a helpful third rule to remember. . . when working with NEGATIVES, imagine a number line in your head, with 0 in the middle. From the right, you have 1-10. To the LEFT of 0, you have negatives. Always remember that while negatives increase in DIGITS the farther you go left, they actually DECREASE in value. For example, -1 will be right after 0, but -10 will be furthest left on the number line. Even though -10 has more digits, it's actually MUCH less in value than -1. This is because -1, if you imagine the number line, is much closer to 0 and the other positive numbers than -10 :). If you remember that, adding and subtracting negatives will be quite easy.

On to the problems. . .

1. x - 6 = - 4

x - 6 + 6 = -4 + 6

x = -4 + 6

x = 2.

First, isolate the variable by getting rid of 6 from the left side of the equation by applying the OPPOSITE of what's presented. Subtraction is presented, so you add. Remember what's done to one side of the equation must be done to the other. The sides of the equation are seperated by the "=" sign. If you imagine where -4 is on the number line, count 6 places towards the POSITIVE side (to the right, closer to 0) because you're adding 6. When you finish your sixth leap, you'll be at positive 2. x=2

2. x + 3 = -7

x + 3 - 3 = -7 - 3

x = - 7 - 3

x = -10

Same rules apply from before. Isolate the variable by applying the opposite. Addition was presented, so we subtract the 3 to get rid of it. Do the same to the other side of the equation. In this case, imagine -7 on the number line. You're SUBTRACTING 3. Remember in normal subtraction, you're DECREASING the value of the number you're subtracting from. On the number line, anything to the right of your number is higher in value, so this means you need to go to the left. Since it's -3, we start at -7 and subtract 3, moving 3 leaps to the left. We land on -10. X = -10.

3. 5x = -2

5x /5 = -2 /5

x = -2/5

(-2/5 is equal to -0.4 in decimal form).

Same rules apply here. Isolate the variable. 5x means you're multiplying the variable by the number hypothetically, which means you must DIVIDE to get rid of the number. One side = the other side, so divide -2 by the same amount. If you know how to convert fractions to decimals, then you know -2/5 = -0.4 as a decimal. x = -0.4

4. 0.5x = 5.

0.5x /0.5 = 5/ 0.5

x = 5/0.5

x = 10.

This one's tricky. Same rules apply, isolate the variable. We apply the same method to both sides of the equation. Here's the tricky part. . . we are left with 5/ .5. It helps if you think of .5 as HALF of 1, and it'll help you even more if you remember that the result of 5/1 = 5.

If 5/ 1 =5, this means that 5/.5, which is HALF of 1, MUST be 10.

If this doesn't help you, then imagine it as money. you have 50 cents, how many of those will it take you to get to $5?? If you count it out, it'll take you 10 stacks of 50 cents to get to $5, double of what it'd take you to get to $5 if you had $1 bills.

This should be everything you need to understand how to solve these 4 problems!!