Question

a) find the value of x when x + 10 = 16:
$x + 10 = 16$
$x = 16$

a) describe the solution of $x + 10 \geq 16$

a) if x is equal to 16, $x + 10$ will be equal to 16.
if x is greater than 16, $x + 10$ will be greater than 16.

graph an inequality to represent all possible values of x;

Explanation:

Part a: Find the value of \( x \) when \( x + 10 = 16 \)

Step 1: Subtract 10 from both sides

To solve for \( x \) in the equation \( x + 10 = 16 \), we use the subtraction property of equality. Subtract 10 from both sides of the equation:
\( x + 10 - 10 = 16 - 10 \)

Step 2: Simplify both sides

Simplifying the left side: \( x + 0 = x \).
Simplifying the right side: \( 16 - 10 = 6 \).
So, \( x = 6 \).

Part b: Describe the solution of \( x + 10 \geq 16 \)

• For \( x + 10 = 16 \), we found \( x = 6 \). So when \( x = 6 \), \( x + 10 = 16 \).
• For \( x + 10 > 16 \), we solve for \( x \) by subtracting 10 from both sides: \( x > 16 - 10 \), so \( x > 6 \). Thus, if \( x \) is greater than 6, \( x + 10 \) is greater than 16.

Part c: Graph the inequality \( x + 10 \geq 16 \) (which simplifies to \( x \geq 6 \))

1. Simplify the inequality: Start with \( x + 10 \geq 16 \). Subtract 10 from both sides: \( x \geq 6 \).
2. Graph on a number line:

• Locate 6 on the number line.
• Since the inequality is \( \geq \), we use a closed (filled) circle at 6 to include the value 6.
• Draw an arrow to the right of 6 to show all values greater than or equal to 6.

Answer:

s:

• Part a: \( \boldsymbol{x = 6} \)
• Part b: If \( x \) is \(\boldsymbol{\text{equal to}}\) 6, \( x + 10 \) will be equal to 16. If \( x \) is \(\boldsymbol{\text{greater than}}\) 6, \( x + 10 \) will be greater than 16.
• Part c: On the number line, draw a closed circle at 6 and an arrow pointing to the right (representing \( x \geq 6 \)).