To tackle the given problem, let's break it down into a clear, step-by-step process.
Step 1: Translate the Problem into an Equation
We are given:
1. A number (let's denote it as [tex]\( x \)[/tex]).
2. This number increased by 11.
3. This result is 2 times the sum of the number and another value (though the value to be added isn't provided here, we'll use the number itself for simplicity).
So, the problem statement can be written as:
[tex]\[ \text{Number} + 11 = 2 (\text{Number} + 6 )\][/tex]
Step 2: Formulate the Equation
To form the equation, we use [tex]\( x \)[/tex] for the number:
[tex]\[ x + 11 = 2(x + 6) \][/tex]
Step 3: Solve the Equation
Now, solve for [tex]\( x \)[/tex]:
1. Distribute the 2 on the right side:
[tex]\[ x + 11 = 2x + 12 \][/tex]
2. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ 11 = x + 12 \][/tex]
3. Subtract 12 from both sides:
[tex]\[ 11 - 12 = x \][/tex]
[tex]\[ -1 = x \][/tex]
So, the solution to the equation is:
[tex]\[ x = -1 \][/tex]
Final Answer
1. The equation is:
[tex]\[ x + 11 = 2(x + 6) \][/tex]
2. The solution is:
[tex]\[ x = -1 \][/tex]
