A number g is decreased by 23 and then multiplied by 0.5 the result is 8 more than twice the number g

Let's denote the number \( g \).

According to the problem, the sequence of operations can be expressed as follows:

1. \( g \) is decreased by 23: \( g - 23 \)
2. The result is then multiplied by 0.5: \( 0.5(g - 23) \)
3. This result is equal to 8 more than twice the number \( g \): \( 8 + 2g \)

We can set up the equation:

\[ 0.5(g - 23) = 8 + 2g \]

Now, let's solve this equation step-by-step.

### Step 1: Expand the left side of the equation
\[ 0.5(g - 23) = 0.5g - 11.5 \]

### Step 2: Set the expanded equation equal to the right side
\[ 0.5g - 11.5 = 8 + 2g \]

### Step 3: Move all terms involving \( g \) to one side of the equation and constants to the other side
\[ 0.5g - 2g = 8 + 11.5 \]

### Step 4: Simplify both sides
\[ -1.5g = 19.5 \]

### Step 5: Solve for \( g \) by dividing both sides by -1.5
\[ g = \frac{19.5}{-1.5} \]
\[ g = -13 \]

So, the value of \( g \) is \(-13\).

Would you like more details or have any questions? Here are some additional related questions for practice:

1. If \( g \) were increased by 10 and then divided by 2, what would the new expression be?
2. What is \( 0.5(g - 23) \) when \( g = -10 \)?
3. Solve \( 3(g + 4) = 2g - 5 \).
4. If the equation were \( 0.5(g - 23) = 10 + 2g \), what would \( g \) be?
5. What is the value of \( g \) if \( g - 23 = 2g + 10 \)?
6. Find \( g \) if \( 2(g - 10) = 3g + 5 \).
7. What is the solution to \( 0.5(g + 10) = 2g - 7 \)?
8. If \( g \) is decreased by 15 and then multiplied by 3, how would you write that expression?

**Tip:** When solving equations, always isolate the variable on one side by using inverse operations to simplify step-by-step.

Learn how to solve equations involving arithmetic operations with a step-by-step solution example. This problem involves algebraic manipulation and arithmetic concepts, suitable for students in Grades 7-9.

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