Math Problem Statement

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

Solution

Let's denote the number gg.

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

  1. gg is decreased by 23: g23g - 23
  2. The result is then multiplied by 0.5: 0.5(g23)0.5(g - 23)
  3. This result is equal to 8 more than twice the number gg: 8+2g8 + 2g

We can set up the equation:

0.5(g23)=8+2g0.5(g - 23) = 8 + 2g

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

Step 1: Expand the left side of the equation

0.5(g23)=0.5g11.50.5(g - 23) = 0.5g - 11.5

Step 2: Set the expanded equation equal to the right side

0.5g11.5=8+2g0.5g - 11.5 = 8 + 2g

Step 3: Move all terms involving gg to one side of the equation and constants to the other side

0.5g2g=8+11.50.5g - 2g = 8 + 11.5

Step 4: Simplify both sides

1.5g=19.5-1.5g = 19.5

Step 5: Solve for gg by dividing both sides by -1.5

g=19.51.5g = \frac{19.5}{-1.5} g=13g = -13

So, the value of gg is 13-13.

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

  1. If gg were increased by 10 and then divided by 2, what would the new expression be?
  2. What is 0.5(g23)0.5(g - 23) when g=10g = -10?
  3. Solve 3(g+4)=2g53(g + 4) = 2g - 5.
  4. If the equation were 0.5(g23)=10+2g0.5(g - 23) = 10 + 2g, what would gg be?
  5. What is the value of gg if g23=2g+10g - 23 = 2g + 10?
  6. Find gg if 2(g10)=3g+52(g - 10) = 3g + 5.
  7. What is the solution to 0.5(g+10)=2g70.5(g + 10) = 2g - 7?
  8. If gg 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.

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Math Problem Analysis

Mathematical Concepts

Equations
Arithmetic operations

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9