Twice a number is 6.

• 2x = 6
• 2+x = 6
• 2(2x) = 6
• 2+2(x)=6

Four added to a number gives ten.

• 4x=10
• x + 4x =10
• 4 + x = 10
• 4 > x = 10

Twenty-five decreased by twice a number is twelve.

• 25 – 2x = 12
•  2x - 25 = 12
• 25 + 2x = 12
• 25x – x = 12

If thrice a number is added to seven, the sum is ninety-eight.

• x + 3 (7) = 98
• 3 + 7x = 98
• 3 + x + 7 = 98
• 3x + 7 = 98

The sum of the squares of a number x and 3 yields 25.

• x² + 3² = 16
• x² - 3² = 16
• (x + 3)² = 16
• 2(x + 3) = 16

The difference between thrice a number and nine is 100. 

• 3 * 9 - x = 100
• 3x – 9 = 100
• x3 - 9 = 100
• 3x + 9 = 100

The sum of two consecutive integers is equal to 25.

• x + 1 (x + 1) = 25
• x + 1 (x + 2) = 25
• x + 1 (x + 3) = 25
• x + (x + 1) = 25

The product of two consecutive integers is 182.

• x(x + 1) = 182
• x + (x + 1) = 182
• x + 1(x + 2) = 182
• x (x + 1)(x + 2)= 182

The area of the rectangle whose length is (x + 4) and width is (x – 3) is 30. 

• (x4)(x – 3) = 30
• (x + 4)(x3) = 30
• 4x(x – 3) = 30
• (x + 4)(x – 3) = 30

The sum of the ages of Mark and Sheila equals 47.

• x + y = 47 
• xy = 47 
• x - y = 47 
• 2(x + y) = 47