Question

PLEASE HELP ME! :(

1. Twice a number increased by 12 is equal to 3 times the number minus 31. Find the number.
2. Twelve decreased by twice a number is -7. What is the number?
3. Three consecutive intergers have a sum of -33. What are the intergers?
4. The sum of 4 times a number and 14 is 16. What is the number?
5. The sum of 3 times a number and 17 is 5. What is the number?

Answer 1

Each of the five mathematical problems is solved using algebraic methods to find the values of the unknown number. The answers are: 43, 9.5, consecutive integers -12, -11, -10; 0.5, and -4 for each problem respectively.

Step-by-step explanation:

Let's solve each problem step-by-step using algebraic methods:

1. For the first problem, let the number be x. The equation following the given statement is 2x + 12 = 3x - 31. Solving this gives x = 43.
2. In the second problem, again let the number be x. So, the equation is 12 - 2x = -7, leading to the solution x = 9.5.
3. For the third problem, if the first integer is n, then the consecutive integers are n, n+1, and n+2. Their sum gives n + (n+1) + (n+2) = -33, yielding n = -12, so the integers are -12, -11, and -10.
4. The fourth problem's equation, with the number as x, is 4x + 14 = 16, which gives x = 0.5.
5. Finally, for the fifth problem, the equation is 3x + 17 = 5, and the solution is x = -4.

All solutions adhere to basic mathematical operations and the rules of addition, multiplication, and solving linear equations.

Answer 2

Here, I'll do the first one for you.
When they are talking about a number, use "x".
Since it says twice a number, you say 2x. Or 3x for three times the number
2x+12=3x-31
Then use algebra to find x. Get the numbers on one side and all the x's on the other.
2x+12+31=3x-31+31
2x+43-2x=3x-2x
x=43

Now do the rest on your own!