Question

When you began your diet, you weighed 154 pounds. After 2 weeks, you weighed 149 pounds. You can express the relationship between your initial weight, final weight, and the change between them by the equation $$154+x=149,$$ where \(x\) represents your change in weight in the 2 weeks. a. Solve the equation for \(x\) b. Was your change in weight a loss or a gain? Explain.

Short answer

Answer: The change in weight was -5 pounds, indicating a weight loss of 5 pounds.

Step-by-step solution

Identify the equation

The given equation representing the relationship between the initial weight, final weight, and the change is: $$154+x=149$$

Isolate x

To find the value of x, we need to isolate it on one side of the equation. To do this, subtract 154 from both sides: $$x = 149 - 154$$

Calculate x

By performing the subtraction, we can find the value of x: $$x = -5$$ #b. Was your change in weight a loss or a gain? Explain#

Observe the value of x

The value of x is -5, which is a negative number.

Interpret the value of x

Since x represents the change in weight and the value is negative, this means that there was a weight loss of 5 pounds. A positive number would have indicated a weight gain.