Solve and check the linear equation.
3(x-2) + 8 = 2(x + 5)

x = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

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

Step 2: Solve for x

(Parenthesis) Distribute:                                                                               3x - 6 + 8 = 2x + 10Combine like terms:                                                                                     3x + 2 = 2x + 10{Subtraction Property of Equality] Subtract 2x on both sides:                    x + 2 = 10[Subtraction Property of Equality] Subtract 2 on both sides:                      x = 8

Step 3: Check

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

Substitute in x:                                                                                               3(8 - 2) + 8 = 2(8 + 5)(Parenthesis) Subtract/Add:                                                                         3(6) + 8 = 2(13)Multiply:                                                                                                         18 + 8 = 26Add:                                                                                                               26 = 26

Here we see that 26 does indeed equal 26.

∴ x = 8 is the solution to the equation.

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