Question

What is the solution to the linear equation?

6k + 10.5 = 3k + 12
O k = 0.5
O k = 2
O k = 7.3
Ok = 9

Answer 1

k = 0.5

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
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients

Explanation:

Step 1: Define

6k + 10.5 = 3k + 12

Step 2: Solve for k

1. [Subtraction Property of Equality] Subtract 3k on both sides: 3k + 10.5 = 12
2. [Subtraction Property of Equality] Subtract 10.5 on both sides: 3k = 1.5
3. [Division Property of Equality] Divide 3 on both sides: k = 0.5

Step 3: Check

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

1. Substitute in k: 6(0.5) + 10.5 = 3(0.5) + 12
2. Multiply: 3 + 10.5 = 1.5 + 12
3. Add: 13.5 = 13.5

Here we see that 13.5 does indeed equal 13.5.

∴ k = 0.5 is the solution to the equation.