Four times the sum of a number and four is the same as two multiplied by two less than three times the number. What is the solution to the problem?

Answer 1

Let the unknown number be represented by \( x \).

We start by translating the problem into mathematical expressions based on the description:

1. The sum of a number and four is \( x + 4 \).
2. Four times this sum is \( 4(x + 4) \).
3. Two less than three times the number is \( 3x - 2 \).
4. Two multiplied by this expression is \( 2(3x - 2) \).

Setting the two expressions equal to each other according to the problem statement:

\[ 4(x + 4) = 2(3x - 2) \]

Now we simplify both sides:

Left side: \[ 4(x + 4) = 4x + 16 \]

Right side: \[ 2(3x - 2) = 6x - 4 \]

Now we have the equation:

\[ 4x + 16 = 6x - 4 \]

Next, we rearrange the equation to isolate \( x \). Start by subtracting \( 4x \) from both sides:

\[ 16 = 2x - 4 \]

Next, add 4 to both sides:

\[ 20 = 2x \]

Now, divide both sides by 2:

\[ x = 10 \]

Thus, the solution to the problem is:

\[ \boxed{10} \]