3/4x+2=7+1/3x
What does x equal?
Please show all work.
I am not certain what you meant...you did not use grouping symbols.
Assuming you meant this
3x/4 + 2=7+ x/3
multipy each side by 12
9x+24=84+4x
subtract 4x from each side, then subtract 24 from each side.
Yes, that is what I meant. Sorry for the confusion. Thank you.
To solve for x in the equation 3/4x + 2 = 7 + 1/3x, we need to isolate the variable x on one side of the equation.
Step 1: Let's start by simplifying the equation. To do this, we can combine like terms.
On the left side, we have 3/4x + 2. On the right side, we have 7 + 1/3x.
Step 2: To combine the fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 4 and 3 is 12. Therefore, we need to multiply the terms by appropriate numbers to make the denominators equal to 12.
Multiplying 3/4x + 2 by 3 and 7 + 1/3x by 4, we get:
(3/4 * 3)x + 3 * 2 = 7 * 4 + (1/3 * 4)x
Simplifying further, we have:
(9/4)x + 6 = 28 + (4/3)x
Step 3: Now, we'll eliminate the fractions by multiplying each term by the common denominator, which is 4 * 3 = 12.
12 * (9/4)x + 12 * 6 = 12 * 28 + 12 * (4/3)x
Simplifying, we get:
27x + 72 = 336 + 16x
Step 4: Let's gather the x terms on one side of the equation and the constant terms on the other side.
Subtracting 16x from both sides, we have:
27x - 16x + 72 = 336
Simplifying further, we get:
11x + 72 = 336
To isolate the x term, we subtract 72 from both sides:
11x + 72 - 72 = 336 - 72
This simplifies to:
11x = 264
Step 5: Finally, to solve for x, we divide both sides of the equation by 11:
11x/11 = 264/11
Simplifying this equation results in:
x = 24
Therefore, the value of x that satisfies the equation 3/4x + 2 = 7 + 1/3x is x = 24.