Explanation: To find the value of x, you have to isolate it on one side of the equation. You can do this by adding or subtracting the number near it, or dividing by its coefficient.
The steps for solving for x are to-
1) Simplify any numbers on one side that can be simplified
Example: 2x + 1 + 2 = 7 In this, 2 and 1 can be simplified to make 3 because they are both whole numbers. This can also be done with coefficients, like adding 4x and 6x on one side of the equation because they have the same variable.
2) Add or subtract the constants from the side with x.
Example: 2x + 3 = 7. Here, you would subtract 3, the constant, from both sides to isolate the x. The answer would be 2x = 4.
3) Divide by the coefficient.
Example: 2x = 4. Here, the coefficient is 2, because it’s the number next to the variable x. You’d divide it from both sides to get the answer x = 2.
Answers:
2x - 5 = 11
Here, to get rid of the -5, we add five to both sides of the equation to make it become 0. The reason you have to do it to BOTH sides is because you need the equation to stay equal.
2x - 5 = 11
(+5) (+5)
2x = 16
Now, the coefficient, 2, needs to be divided from both sides to isolate the x.
2x = 16
(/2) (/2)
x = 8
Here, the answer is that x = 8!
13 = -4x + 9
Here, once again, we first have to subtract from the side with the x on it before we divide. Because this number is a positive nine, we have to subtract 9 to get to zero, rather than how we added when we had a negative number.
13 = -4x + 9
(-9) (-9)
4 = -4x
Now, we are left with a coefficient of -4. When you divide this coefficient, you have to remember to keep in the negative, rather than dividing by 4.
4 = -4x
(/-4) (/-4)
-1 = x
The solution to this equation is that x = -1
7 - 3x = 34
First we have to subtract seven from both sides, because the seven in this equation is positive.
7 - 3x = 34
(-7) (-7)
-3x = 27
(Note that -3x is a negative number. This is because there was a subtraction mark in front of it.)
Now, we divide both sides by the coefficient, which is -3, to isolate the x
-3x = 27
(/-3) (/-3)
x = -9
In this equation, x is -9.
11 = x - 5 + 8
First, we simplify the (5 + 8) into one number
11 = x - 13
Then we add 13 to both sides to isolate the x
11 = x - 13
(+13) (+13)
24 = x
Because there is no coefficient, this equation ends here, and x is 24!
-14x + 3 = 12
(-3) (-3)
-14x = 9
(/-14) (/-14)
x = -9/14
Here, because you can’t make a whole number, you’d simplify the answer of x to be the fraction -9/14, because you are dividing 9 by -14.
6) To set up this equation, we have to identify the constants and coefficient.
- To start, we will use the variable x to be our unknown number for how many weeks he needs before he can buy the TV.
- We know his end goal is 1664, so that will be our answer.
- Our coefficient for x will be 60, because that’s how much money he’ll be getting each week.
- Our coefficient for the side of x will be 500, because he already has that fixed amount of money that can’t be altered by the variable x.
- Our equation will end up looking like this:
60x + 500 = 1664
(-500) (-500)
60x = 1164
(/60) (/60)
x = 19.4
Now, 19.4 isn’t a whole number. Since the number is over 19, we would round up to 20 because he needs a full week to put in the money.
So, in this equation, it would take him 20 weeks to buy the TV.
7) Let’s identify our values for this one.
The value for the unknown, how many values James can drive, will be x.
The total money he has is 250, so that will be our answer.
It costs 6$ per hour, so 6 will be our coefficient
The initial cost is 52$, so that will be the value on our x side.
The equation should look like:
6x + 52 = 250
(-52) (-52)
6x = 198
(/6) (/6)
x = 33
In this equation, James can drive his rental car for 33 hours!
8) Let’s identify the values for this one!
- Our unknown, how many hours Aislyn rented the room, will be represented by x
- Since it’s 5$ for each hour, our coefficient will by 5.
- An initial fee of 30$ means 30 will be our constant on the x side
- 50$ total means 50 will be on the opposite side of x.
The equation should look like:
5x + 30 = 50
(-30) (-30)
5x = 20
(/5) (/5)
x = 4
So, Aislyn rented the room for 4 hours!!
Hope this helps.