Math Problem Statement

Make this equation true by adding parentheses

3+2 to the power of 2-5 multipy 4-2/2+3=23

Solution

To make the equation true by adding parentheses, the key is to group operations in a way that satisfies the given result. The equation is:

3+225×42/2+3=233 + 2^2 - 5 \times 4 - 2/2 + 3 = 23

By adding parentheses, the equation can be rewritten as:

3+(225)×(42/2)+3=233 + (2^2 - 5) \times (4 - 2/2) + 3 = 23

Let's simplify step-by-step:

  1. First, calculate the exponents:
    22=42^2 = 4

  2. Replace the value and simplify inside the first parentheses:
    3+(45)×(41)+33 + (4 - 5)\times(4 - 1) + 3

  3. Calculate inside the second parentheses:
    3+(1)×(3)+33 + (-1)\times(3) + 3

  4. Multiply:
    33+3+3=63 - 3 + 3 + 3 = 6

The parentheses are incorrect. However, we can attempt another grouping that would satisfy the equation:

3+((225)×(4(2/2)))+3=233 + ((2^2 - 5) \times (4 - (2/2))) + 3 = 23

This simplifies to:

  1. Calculate 22=42^2 = 4, so: 3+((45)×(41))+3=233 + ((4 - 5) \times (4 - 1)) + 3 = 23

  2. Simplifying further: 3+(1×3)+3=233 + (-1 \times 3) + 3 = 23

Again, this is incorrect. Let's try the following grouping:

3+(225)×(42)/2+3=233 + (2^2 - 5) \times (4 - 2)/2 + 3 = 23

This simplifies to:

  1. Calculate 22=42^2 = 4, so: 3+(45)×22/2+3=233 + (4 - 5) \times 2 - 2/2 + 3 = 23

  2. Simplify further: 3+(1×2)1+3=233 + (-1 \times 2) - 1 + 3 = 23

This still doesn't yield 23. Given the complex nature of the operations, if there's a specific expected outcome or other constraints, I may need those details to determine the correct placement of parentheses.

Would you like to provide more details, or should I keep refining this? Here are some questions to deepen understanding:

  1. Should the solution strictly use all operations?
  2. Can I add parentheses in multiple places?
  3. Is this a school assignment?
  4. Would you like a breakdown of each potential operation?
  5. Are you looking for other possible solutions?

Tip: When adding parentheses, start by identifying the highest priority operation in the desired outcome equation.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Exponents
Arithmetic Operations

Formulas

Order of Operations (PEMDAS/BODMAS)
Exponentiation

Theorems

PEMDAS/BODMAS

Suitable Grade Level

Grades 6-8