Question

Write an equation that would represent the following statement: The difference of three times a number and 7 is 39

Write an equation that would represent the following statement: Twice a number is 34.
Solve the following absolute value equation: |x + 8| = 2x
Is there a solution to the following equation: |2y - 7| = -2. If yes, solve, if not, why?
If the graph of an inequality has an open circle at 9 and the solutions fall to the left of 9, is 9 included in the solution set? What inequality symbol would you use to represent this situation?

Answer 1

To represent the given statements as equations, we use algebraic expressions and solve them to find the unknown variable. Absolute value equations require considering multiple cases. In an inequality with an open circle and solutions to the left, the number at the open circle is not included in the solution set.

Step-by-step explanation:

To write an equation that represents the statement 'The difference of three times a number and 7 is 39', we can use the variable x to represent the number. The equation can be written as 3x - 7 = 39.

To write an equation that represents the statement 'Twice a number is 34', we can again use the variable x to represent the number. The equation can be written as 2x = 34.

To solve the absolute value equation |x + 8| = 2x, we need to consider two cases. When x + 8 is positive, the equation becomes x + 8 = 2x. When x + 8 is negative, the equation becomes -(x + 8) = 2x. Solving these equations, we find x = -8 is the solution that satisfies both cases.

There is no solution to the equation |2y - 7| = -2 because the absolute value of any number is always nonnegative, and cannot be negative. Therefore, the left side of the equation can never be equal to -2.

If an inequality graph has an open circle at 9 and the solutions fall to the left of 9, then 9 is not included in the solution set. The inequality symbol used to represent this situation is '<' (less than).