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 \( x=7 \).

Let's correct the equation based on the problem statement. The number \( x \) increased by 9 is described as: \[ x + 9 = 2(x + 1) \] Now, let's simplify the equation. Expanding the right side gives us: \[ x + 9 = 2x + 2 \] Next, subtract \( x \) from both sides: \[ 9 = x + 2 \] Now, subtract 2 from both sides: \[ x = 7 \] So the equation correctly leads to the solution \( x = 7 \). In a fun twist, if you think of \( x \) as an adventurous treasure hunter, then finding the value of \( x \) is like solving a riddle to uncover the treasure! Keep noting where the numbers go, and soon you'll find the hidden gems! Additionally, if you ever face problems with equations, remember that writing down each step clearly is your buddy! Common mistakes often include skipping steps or forgetting to distribute correctly, so take it slow, and you will outsmart those pesky math gremlins.