x/2 + x/4 = 1
the answer is 1 1/3
can you show me the method please
thanks in advance :)
start by multiplying by the lowest common denominator (in this case 4), simplify, then solve.
4(x/2) + 4(x/4)= 1
4/2=2 and 4/4 =1, therefore:
2x + x = 1
3x = 1
(3x)/3 = 1/3
x= 1/3
Rachel forgot to multiply the right side by 4, her equation should have been
2x + x = 4
3x = 4
x = 4/3 or 1 1/3
The book states that the answer is one and a third
i got the same answer as Rachel
Ummmh,
wasn't Rachel's answer 1/3
and mine was 1 1/3 ??
Certainly! To solve the equation x/2 + x/4 = 1, we can follow a few steps:
Step 1: Find a common denominator.
Since the denominators in the given equation are 2 and 4, the least common multiple (LCM) of 2 and 4 is 4. So, we'll convert the numerator and denominators to have 4 as the common denominator.
Rewriting the equation, we have 2x/4 + x/4 = 1.
Step 2: Combine the like terms.
Now that the denominators are the same, we can combine the numerators. The combined numerator is (2x + x) = 3x. So our equation becomes 3x/4 = 1.
Step 3: Isolate the variable.
To solve for x, we need to isolate it on one side of the equation. In this case, we can achieve that by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3.
(4/3) * (3x/4) = (4/3) * 1
The 3's cancel out on the left side, leaving us with x. And on the right side, 4/3 multiplied by 1 gives us 4/3.
x = 4/3
Step 4: Simplify the answer, if necessary.
The answer, 4/3, can be simplified further. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 3 is 1. So dividing 4 and 3 by 1, the simplified answer is:
x = 4/3 = 1 1/3.
Therefore, the solution to the equation x/2 + x/4 = 1 is x = 1 1/3.