Question

3(x − 1) − (x + 5) = 2

Answer 1

\[ 3(x − 1) − (x + 5) = 2\]distribute the \(3\) and the \(-\) sign (Distributive Property of Equality):\[3x-3-x-5=2\]combine like terms (Substitution Property of Equality):\[2x-8=2\]add \(8\) to both sides (Addition Property of Equality):\[2x=10\]divide both sides by \(2\) (Division Property of Equality):\[x=5\]

check your answer!\[ 3(x − 1) − (x + 5) = 2\]\[3(5-1)-(5+5)=2\]\[3(4)-(10)=2\]\[12-10=2\]\[2=2~\checkmark\]

Answer 2

3(x-1) - (x+5) = 2

Following 'Please Excuse My Dear Aunt Sally' or 'Parentheses, Exponents, Multiplication and Division, Addition and Subtraction', we must first simplify the parentheses. First, multiply the constants in front of the parentheses across the contents of the parentheses if possible.

However, the contents of the parentheses are already simplified. Next we look for exponents; there are none. Now we do multiplication.

When you multiply any constant times a term in parentheses, you must multiply the constant times every item bounded by the parentheses.

So in this case, we need to take 3 times both x and -1.

3(x-1) - (x+5) = 2
becomes
3(x) + 3(-1) - (x+5) = 2

Now I will simplify the 3(x) and 3(-1):

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

The (x+5) term might not look like it has a constant in front of it, but it does: the constant is -1, because the (x+5) term is being subtracted Let us rewrite it from '- (x+5)' to '+ (-1)(x+5) to reflect that hidden constant.

3x - 3 + (-1)(x+5) = 2

Now, we once again distribute the constant across the items in parentheses:

3x - 3 + (-1)(x) + (-1)(5) = 2

Applying the multiplication:

3x - 3 + -x + -5 = 2

'+ -x' and '+ - 5' is the same as '- x' and '- 5':

3x - 3 - x - 5 = 2

Now we can rearrange the equation to group 'x' terms and 'constant' terms, because addition is commutative. I will group the 'x' terms on the left, and the 'constant' terms on the right.

3x - x - 3 - 5 = 2

Now we can perform addition and subtraction.

3x - x = 2x

-3 - 5 = - 8

2x - 8 = 2

In an equation, you can perform addition on both sides, and the new equation will still be true. So now I will add 8 to both sides:

2x - 8 + 8 = 2 + 8

Simplifying the left side:
2x - 8 + 8 = 2x

Right side:
2 + 8 = 10

which yields a new equation of:

2x = 10

We can divided both sides by 2, to find the final value of x:

2x/2 = 10/2

2 x / 2 = x

10 / 2 = 5

Therefore: x = 5