Consider the equation below.
1/5(x+2)+2x = 6x-10
Part A: Which property can be used to simplify the expression 1/5(x+2)?
Answer _______________
Part B: Move all x-terms to one side of the equation and simplify.
Show your work.
Answer _______________
Part C: what is the value of x?
show your work.
Answer: ____________
Distributive property
9x
Part A: To simplify the expression 1/5(x+2), you can use the distributive property.
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
In the given expression, 1/5 is multiplied by (x + 2). So, using the distributive property, we can rewrite the expression as:
1/5(x + 2) = (1/5) * x + (1/5) * 2
Simplifying further gives:
1/5(x + 2) = (1/5)x + 2/5
Therefore, the property used to simplify the expression 1/5(x + 2) is the distributive property.
Answer: Distributive Property
Part B: To move all x-terms to one side of the equation, we can start by subtracting 6x from both sides of the equation:
1/5(x + 2) + 2x - 6x = 6x - 10 - 6x
Simplifying gives:
1/5(x + 2) - 4x = -10
Next, let's simplify the expression 1/5(x + 2). Using the distributive property as we did in Part A, we have:
1/5(x + 2) = (1/5)x + (1/5)2 = (1/5)x + 2/5
Substituting this back into the equation, we get:
(1/5)x + 2/5 - 4x = -10
Combine the x-terms by subtracting (1/5)x from both sides of the equation:
(1/5)x - (1/5)x + 2/5 - 4x = -10 - (1/5)x
Simplifying further gives:
2/5 - 4x = -10 - (1/5)x
To simplify the equation, we can multiply all terms by 5. This will eliminate the fractions:
(5)(2/5) - (5)(4x) = (5)(-10) - (5)(1/5)x
Simplifying gives:
2 - 20x = -50 - x
Now, let's move all x-terms to one side by adding 20x to both sides of the equation:
2 - 20x + 20x = -50 - x + 20x
Simplifying further gives:
2 = -50 + 19x
Finally, subtract -50 from both sides of the equation:
2 + 50 = -50 + 19x + 50
Simplifying:
52 = 19x
Therefore, after moving all x-terms to one side of the equation and simplifying, we have:
52 = 19x
Answer: 52 = 19x
Part C: To find the value of x, divide both sides of the equation by 19:
52/19 = 19x/19
Dividing gives:
x = 52/19
Hence, the value of x is 52/19.
Answer: x = 52/19