Question

(07.03)

An equation is shown below:

5(2x - 8) + 15 = -15

Write the steps you will use to solve the equation and explain each step.

Answer 1

Answer: x=1

Explanation:

Let's solve your equation step-by-step.

5(2x−8)+15=−15

Step 1: Simplify both sides of the equation.

5(2x−8)+15=−15

(5)(2x)+(5)(−8)+15=−15(Distribute)

10x+−40+15=−15

(10x)+(−40+15)=−15(Combine Like Terms)

10x+−25=−15

10x−25=−15

Step 2: Add 25 to both sides.

10x−25+25=−15+25

10x=10

Step 3: Divide both sides by 10.

10x/10=10/10

x=1

Answer 2

x = 1

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

5(2x - 8) + 15 = -15

Step 2: Solve for x

1. [Subtraction Property of Equality] Subtract 15 on both sides: 5(2x - 8) = -30
2. [Division Property of Equality] Divide 5 on both sides: 2x - 8 = -6
3. [Addition Property of Equality] Add 8 on both sides: 2x = 2
4. [Division Property of Equality] Divide 2 on both sides: x = 1

Step 3: Check

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

1. Substitute in x: 5(2(1) - 8) + 15 = -15
2. (Parenthesis) Multiply: 5(2 - 8) + 15 = -15
3. (Parenthesis) Subtract: 5(-6) + 15 = -15
4. Multiply: -30 + 15 = -15
5. Add: -15 = -15

Here we see that -15 does indeed equal -15.

∴ x = 1 is the solution to the equation.