Write an equation and solve. A number increased by 9 is 2 times the sum of the number and 1 . The equation is \( x+9=2 \). (Type an equation using \( x \) as the variable.) The solution is \( x=7 \).

It looks like there's a slight error in the equation you've provided. Let's break down the problem step by step to ensure accuracy. ## Problem Statement *A number increased by 9 is 2 times the sum of the number and 1.* ## Translating the Statement into an Equation 1. **Identify the unknown number**: Let's denote the unknown number as \( x \). 2. **"A number increased by 9"**: This translates to \( x + 9 \). 3. **"2 times the sum of the number and 1"**: First, find the sum of the number and 1, which is \( x + 1 \). Then, multiply this sum by 2, resulting in \( 2(x + 1) \). 4. **Setting them equal**: According to the problem, the first expression is equal to the second. Therefore, the correct equation is: \[ x + 9 = 2(x + 1) \] ## Solving the Equation Let's solve for \( x \): 1. **Expand the right side**: \[ x + 9 = 2x + 2 \] 2. **Subtract \( x \) from both sides**: \[ 9 = x + 2 \] 3. **Subtract 2 from both sides**: \[ 9 - 2 = x \] \[ 7 = x \] ## Solution The value of the number is: \[ x = 7 \]