Can someone help me with this please? I am trying to find the solution for
5/4x + 1/8x = 5/8 + x
x = ?
Please use parentheses to reduce ambiguity in the equations.For example,
5/(4x) is not the same as (5/4)*x.
Get a common denomiatore for the x terms and collect them on one side of the equation.
5/4 x + 1/8 x - x = (10 +1 -8)x/8 = 3x/8. That gives you
3/8 x = 5/8
Then multiply both sides of the equation by 8/3
Would the answer be x=5/3?
Of course, I can help you solve the equation! This equation is a linear equation involving fractions, so the first step is to eliminate the fractions by multiplying every term by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 8x.
Let's go through the steps together:
1. Multiply every term by the LCD, 8x:
(8x) * (5/4x) + (8x) * (1/8x) = (8x) * (5/8) + (8x) * x
2. Simplify each term:
10 + 1 = 5x + 8x^2
3. Combine like terms:
11 = 13x + 8x^2
4. Rearrange the equation to set it equal to zero:
8x^2 + 13x - 11 = 0
Now that we have a quadratic equation, we can solve it by factoring or by using the quadratic formula. In this case, factoring can be a little bit tricky, so we will use the quadratic formula.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 8, b = 13, and c = -11.
5. Substitute the values into the quadratic formula:
x = (-(13) ± √((13)^2 - 4 * 8 * (-11))) / (2 * 8)
6. Simplify:
x = (-13 ± √(169 + 352)) / 16
x = (-13 ± √521) / 16
Therefore, the two solutions to the equation are:
x1 = (-13 + √521) / 16
x2 = (-13 - √521) / 16
So, the value of x can be either x1 or x2, depending on the situation.