Question

8x - (2x - 13) = 42
solve and check the equation​

Answer 1

x = 29/6

Explanation:

solve for x.

8x - ( 2x - 13 ) = 42

distribute minus sign

8x - 2x + 13 = 42

combine like terms

6x + 13 = 42

subtract 13 from both sides

6x + 13 - 13 = 42 - 13

6x = 29

Divide each side by 6

6x / 6 = 29 / 6

x = 29 / 6

Check the equation :

8x - ( 2x - 13 ) = 42

substitute the value of x in equation

8 ( 29/6) - ( 2(29/6) - 13) = 42

reduce the number with the greatest common factor 2

4 × 29 /3 - ( (29/3) - 13) = 42

calculate the product

116/3 - ( 29/3 - 13 )= 42

calculate the difference

116/3 -( -10/3 )= 42

change the sign

116/3 + 10/3 = 42

add the fractions to get 42.

42 = 42

Hence, verified.

Answer 2

x = 29/6

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

Distributive Property

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

Identify

8x - (2x - 13) = 42

Step 2: Solve for x

1. [Distributive Property] Distribute negative: 8x - 2x + 13 = 42
2. [Subtraction] Combine like terms: 6x + 13 = 42
3. [Subtraction Property of Equality] Subtract 13 on both sides: 6x = 29
4. [Division Property of Equality] Divide 6 on both sides: x = 29/6

Step 3: Check

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

1. Substitute in x: 8(29/6) - [2(29/6) - 13] = 42
2. Multiply: 116/3 - [29/3 - 13] = 42
3. [Brackets] Subtract: 116/3 - -10/3 = 42
4. Subtract: 42 = 42

Here we see 42 does indeed equal 42.

∴ x = 29/6 is the solution.