Question

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Answer 1

b. -84

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Algebra I

• Terms/Coefficients

Explanation:

Step 1: Define

`\displaystyle (a)/(-7) - 7 = 5`

Step 2: Solve for a

1. Addition Property of Equality:
   `\displaystyle (a)/(-7) - 7 + 7 = 5 + 7`
2. [Simplify] Add:
   `\displaystyle (a)/(-7)= 12`
3. Multiplication Property of Equality:
   `\displaystyle -7 \cdot (a)/(-7) = 12 \cdot -7`
4. [Simplify] Multiply:
   `\displaystyle a = -84`

Step 3: Check

Plug in a into the original equation to verify it's a solution.

1. Substitute in a:
   `\displaystyle (-84)/(-7) - 7 = 5`
2. [Frac] Divide:
   `\displaystyle 12 - 7 = 5`
3. Subtract:
   `\displaystyle 5 = 5`

Here we see that 5 does indeed equal 5.

∴ a = -84 is the solution to the equation.