Question

Four times the sum of a number and four is the same as 2×2 less than three times the number

Answer 1

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

The problem states that "four times the sum of a number and four" can be expressed mathematically as:
\[
4(x + 4)
\]

The statement "2×2 less than three times the number" can be written as:
\[
3x - 2 \times 2 = 3x - 4
\]

Now, we can set up the equation based on the information provided:
\[
4(x + 4) = 3x - 4
\]

Next, we will simplify and solve for \( x \).

First, expand the left side:
\[
4x + 16 = 3x - 4
\]

Now, subtract \( 3x \) from both sides:
\[
4x - 3x + 16 = -4
\]
\[
x + 16 = -4
\]

Next, subtract 16 from both sides:
\[
x = -4 - 16
\]
\[
x = -20
\]

Thus, the number is \( \boxed{-20} \).

To verify, we can plug \( x = -20 \) back into the original statements:

1. Calculate \( 4(-20 + 4) \):
\[
4(-20 + 4) = 4(-16) = -64
\]

2. Calculate \( 3(-20) - 4 \):
\[
3(-20) - 4 = -60 - 4 = -64
\]

Since both sides are equal, the solution \( x = -20 \) is confirmed correct.