Twice a number increased by 11 is equal to 32 less than three times the number. Find out the number.
Let x = the number. Now translate every part of the sentence. Twice a number increased through 11 is 2x + 11; 32 less than 3 times a number is 3x - 32. Set the expressions equal to each other: 2x + 11 = 3x - 32. Subtract 2x from both sides of the equation: 2x - 2x + 11 = 3x - 2x - 32. Simplify: 11 = x - 32. Add 32 to both sides of the equation: 11 + 32 = x - 32 + 32. The variable is now alone: x = 43.