Simplify the expression.

To simplify the expression \(2(3x + 4) - 3(2x - 2) + 8(x - 5)\), we'll distribute and combine like terms step by step.

1. Distribute \(2\) in \(2(3x + 4)\): \[ 2 \cdot 3x + 2 \cdot 4 = 6x + 8 \]

2. Distribute \(-3\) in \(-3(2x - 2)\): \[ -3 \cdot 2x + (-3) \cdot (-2) = -6x + 6 \]

3. Distribute \(8\) in \(8(x - 5)\): \[ 8 \cdot x - 8 \cdot 5 = 8x - 40 \]

Now, we'll combine all the results: \[ 6x + 8 - 6x + 6 + 8x - 40 \]

Next, combine the \(x\) terms: \[ 6x - 6x + 8x = 8x \]

Now, combine the constant terms: \[ 8 + 6 - 40 = 14 - 40 = -26 \]

Putting it all together, we have: \[ 8x - 26 \]

Thus, the simplified expression is: \[ \boxed{8x - 26} \]

Write an equation and solve: Four times a number, decreased by 4 is 8.(1 point)
Responses

3
3

1
1

48
48

16
16

Let's represent the unknown number with a variable, say \( x \).

According to the problem, the equation can be written as:

\[ 4x - 4 = 8 \]

Now, we will solve for \( x \):

1. First, add 4 to both sides of the equation: \[ 4x - 4 + 4 = 8 + 4 \] This simplifies to: \[ 4x = 12 \]

2. Next, divide both sides by 4: \[ x = \frac{12}{4} \] This simplifies to: \[ x = 3 \]

So, the solution is:

\[ \boxed{3} \]