Four times the sum of a number and four is the same as two multiplied by two less than three times the number

Answer 1

Let's denote the unknown number as \( x \).

According to the problem, the equation can be set up as follows:

1. Four times the sum of the number and four: \( 4(x + 4) \)
2. Two multiplied by two less than three times the number: \( 2(3x - 2) \)

Now, we can write the equation:

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

Next, we can simplify both sides of the equation.

Starting with the left side:

\[ 4(x + 4) = 4x + 16 \]

Now simplifying the right side:

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

So the equation becomes:

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

Next, we will solve for \( x \). First, we can subtract \( 4x \) from both sides:

\[ 16 = 2x - 4 \]

Now add \( 4 \) to both sides:

\[ 20 = 2x \]

Finally, divide by \( 2 \):

\[ x = 10 \]

Thus, the number is \( \boxed{10} \).

To verify, we can substitute \( x = 10 \) back into the original conditions:

1. Left side: \( 4(10 + 4) = 4 \times 14 = 56 \)
2. Right side: \( 2(3 \times 10 - 2) = 2(30 - 2) = 2 \times 28 = 56 \)

Both sides are equal, confirming that \( x = 10 \) is indeed the correct solution.