Solve for the value of x: x/2 + x/3 = 2x/5 + 3 , also I need a very thorough explanation for this.
1 answer:
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"Isolate the constant by adding 7 to both sides of the equation."
This step separates the non-squareable 7 and the squareable
.
"Add 9 to both sides of
to form a perfect square trinomial while keeping the equation balanced."
After separating the non-squareable, add the number which makes the first or left side a perfect square trinomial. The formula to find the number is:
.
When we plug the values:
Simplify:
"Write the trinomial
as 
squared."
When you factor , you will get 
.
"Use the square root property of equality to get
."
The 16 is coming from the part when we add 9. We needed 9 on the left side for a perfect square, but to protect the balance of the equality, we need to add 9 to the right side too. When we add 7 and 9, we got 16, and that is where it came from.
"Isolate the variable x to get solutions of -1 and 7."
To isolate x we branched the plus-minus sign:
This step separates the non-squareable 7 and the squareable
"Add 9 to both sides of
After separating the non-squareable, add the number which makes the first or left side a perfect square trinomial. The formula to find the number is:
When we plug the values:
Simplify:
"Write the trinomial
When you factor
"Use the square root property of equality to get
The 16 is coming from the part when we add 9. We needed 9 on the left side for a perfect square, but to protect the balance of the equality, we need to add 9 to the right side too. When we add 7 and 9, we got 16, and that is where it came from.
"Isolate the variable x to get solutions of -1 and 7."
To isolate x we branched the plus-minus sign: