1.twice a number is 6

2.four added to a number gives ten
3.twenty five decreased by twice a number twelve
4.if thrice a number added to seven,the sum is ninety eigth
5.the sun of the squares of a number x and 3yields 25
6.the difference between thrice a number ang 9 is 100
7.the sum of two consecutive integers os equalcto25
8.the product of two consecutive integers is 182
9.the area of a rectangle whose length is(x+4) and width is (x-3) is 30
10.the sum af the ages of Mark and Sheila equals 47

2b=6

What number added to −70 has a sum of zero?

What number added to −70 has a sum of zero?

To solve these equations, we can use algebraic techniques. Let's solve each equation step by step:

1. Twice a number is 6:
Let's assume the number is represented by x. The equation can be written as:
2x = 6
To find the value of x, divide both sides of the equation by 2:
x = 6/2
x = 3

2. Four added to a number gives ten:
Again, let's assume the number is x. The equation can be represented as:
x + 4 = 10
To find the value of x, subtract 4 from both sides of the equation:
x = 10 - 4
x = 6

3. Twenty-five decreased by twice a number is twelve:
Assuming the number is x, the equation can be written as:
25 - 2x = 12
To find the value of x, subtract 25 from both sides of the equation and divide by -2:
-2x = 12 - 25
-2x = -13
x = -13/-2
x = 6.5

4. If thrice a number added to seven, the sum is ninety-eight:
Assuming the number is x, the equation can be represented as:
3x + 7 = 98
To find the value of x, subtract 7 from both sides of the equation and divide by 3:
3x = 98 - 7
3x = 91
x = 91/3
x = 30.33 (rounded to two decimal places)

5. The sum of the squares of a number x and 3 yields 25:
Assume the number is x, the equation can be written as:
x^2 + 3^2 = 25
Simplify the equation:
x^2 + 9 = 25
To find the value of x, subtract 9 from both sides of the equation:
x^2 = 25 - 9
x^2 = 16
x = √16
x = 4 or x = -4 (since both the positive and negative square roots of 16 are 4 and -4)

6. The difference between thrice a number and 9 is 100:
Let's assume the number is x, the equation can be represented as:
3x - 9 = 100
To find the value of x, add 9 to both sides of the equation and divide by 3:
3x = 100 + 9
3x = 109
x = 109/3
x = 36.33 (rounded to two decimal places)

7. The sum of two consecutive integers is equal to 25:
Assuming the first integer is x, the second integer will be (x + 1) since they are consecutive. The equation can be represented as:
x + (x + 1) = 25
Combine like terms:
2x + 1 = 25
To find the value of x, subtract 1 from both sides of the equation:
2x = 25 - 1
2x = 24
x = 24/2
x = 12
So, the two consecutive integers are 12 and 13.

8. The product of two consecutive integers is 182:
Assuming the first integer is x, the second integer will be (x + 1) since they are consecutive. The equation can be written as:
x(x + 1) = 182
Expand and simplify the equation:
x^2 + x = 182
To find the value of x, move all terms to one side of the equation and solve the quadratic equation:
x^2 + x - 182 = 0
Using factoring, the equation can be rewritten as:
(x - 13)(x + 14) = 0
Setting each factor equal to zero:
x - 13 = 0 or x + 14 = 0
x = 13 or x = -14
So, the two consecutive integers are 13 and 14, or -14 and -13.

9. The area of a rectangle whose length is (x + 4) and width is (x - 3) is 30:
Assuming x represents the unknown side length, the equation can be written as:
(x + 4)(x - 3) = 30
Expanding the equation:
x^2 + x - 12 = 30
To find the value of x, move all terms to one side of the equation and solve the quadratic equation:
x^2 + x - 12 - 30 = 0
x^2 + x - 42 = 0
Using factoring, the equation can be rewritten as:
(x + 7)(x - 6) = 0
Setting each factor equal to zero:
x + 7 = 0 or x - 6 = 0
x = -7 or x = 6
Since the length of a rectangle cannot be negative, the side length (x) will be 6.

10. The sum of the ages of Mark and Sheila equals 47:
Let's assume Mark's age is represented by x, while Sheila's age is represented by y. The equation can be written as:
x + y = 47
However, since we do not have any additional information, we cannot solve for specific values for x and y.