Question

problem 1: write an addition (+) inequality using the symbol >. a. solve the inequality. b. explain the process of solving the inequality c. draw the inequality on the number line d. write key words or phrases that match the symbol

Explanation:

Step1: Create an addition inequality

Let's create an inequality, for example, \(x + 3>5\).

Step2: Solve the inequality (for part A)

To solve \(x + 3>5\), we subtract 3 from both sides of the inequality. According to the subtraction property of inequalities, if \(a + b>c\), then \(a>c - b\) when we subtract \(b\) from both sides.
So, \(x+3 - 3>5 - 3\), which simplifies to \(x > 2\).

Step3: Explain the process (for part B)

The process of solving a linear inequality like \(x + 3>5\) is similar to solving a linear equation, but we have to be careful with multiplying or dividing by negative numbers (which we didn't do here). We use the properties of inequalities: adding or subtracting the same number from both sides of an inequality does not change the direction of the inequality sign. So we subtract 3 from both sides to isolate \(x\), resulting in \(x>2\).

Step4: Draw on the number line (for part C)

To draw \(x > 2\) on the number line:

• First, draw a number line with a scale that includes 2.
• Then, place an open circle at 2 (because \(x\) is not equal to 2, only greater than)
• Finally, draw an arrow to the right of 2 to represent all the numbers greater than 2.

Step5: Key words (for part D)

Key words or phrases that match the symbol \(>\) are "greater than", "more than", "exceeds", etc.

Answer:

• Inequality: \(x + 3>5\)
• Solution (part A): \(x>2\)
• Process Explanation (part B): Subtract 3 from both sides using inequality properties, get \(x>2\)
• Number Line (part C): Open circle at 2, arrow to the right
• Key Words (part D): "greater than", "more than", "exceeds"