Question

state whether each sentence is true or false. if false, replace the underlined term to make a true sentence. 1. in order to write an equation to solve a problem, identify the unknown for which you are looking and assign a(n) number to it. 2. to solve an equation means to find the value of the variable that makes the equation true. 3. the numbers 10, 12, and 14 are an example of consecutive even integers. 4. the absolute value of any number is simply the distance the number is away from zero on a number line. 5. a(n) equation is a comparison of two numbers by division. 6. an equation stating that two ratios are equal is called a(n) proportion. 7. if the new number is less than the original number, the percent of change is a percent of increase. 8. the weighted average of a set of data is the sum of the product of the number of units and the value per unit divided by the sum of the number of units.

Explanation:

Step1: Analyze sentence 1

In writing an equation, we assign a variable, not a number, to the unknown. So it's false.

Step2: Analyze sentence 2

The definition of solving an equation is to find the variable - value that makes the equation true. So it's true.

Step3: Analyze sentence 3

Consecutive even integers have a difference of 2 between each pair. 10, 12, 14 fit this. So it's true.

Step4: Analyze sentence 4

The absolute - value of a number is its distance from zero on the number line. So it's true.

Step5: Analyze sentence 5

A comparison of two numbers by division is a ratio, not an equation. So it's false.

Step6: Analyze sentence 6

An equation stating two ratios are equal is a proportion. So it's true.

Step7: Analyze sentence 7

If the new number is less than the original, it's a percent of decrease, not increase. So it's false.

Step8: Analyze sentence 8

The weighted average is calculated as described. So it's true.

Answer:

1. False, replace "number" with "variable".
2. True
3. True
4. True
5. False, replace "equation" with "ratio".
6. True
7. False, replace "increase" with "decrease".
8. True