Solve the Fraction Equation: Finding X in (2/3)x + 1/4 = 3/4

Question

Find the value of the parameter X

23x+14=34 \frac{2}{3}x+\frac{1}{4}=\frac{3}{4}

Video Solution

Solution Steps

00:00 Solve
00:03 We want to isolate the unknown X
00:08 Let's arrange the equation so that one side has only the unknown X
00:18 Let's simplify what we can
00:24 Let's write as a single fraction
00:32 Let's isolate the unknown X and calculate
00:36 Let's multiply by the reciprocal fraction to eliminate the fraction
00:47 Let's simplify what we can
00:51 And this is the solution to the question

Step-by-Step Solution

Let's proceed with solving the equation step by step:

  1. Start with the equation 23x+14=34 \frac{2}{3}x + \frac{1}{4} = \frac{3}{4} .

  2. Subtract 14 \frac{1}{4} from both sides to remove the constant term on the left:
    23x+1414=3414 \frac{2}{3}x + \frac{1}{4} - \frac{1}{4} = \frac{3}{4} - \frac{1}{4} .

  3. This simplifies to: 23x=3414 \frac{2}{3}x = \frac{3}{4} - \frac{1}{4} .

  4. Perform the subtraction on the right-hand side:
    23x=24=12 \frac{2}{3}x = \frac{2}{4} = \frac{1}{2} .

  5. Now solve for x x by dividing both sides of the equation by 23 \frac{2}{3} :
    x=12÷23 x = \frac{1}{2} \div \frac{2}{3} .

  6. Dividing by a fraction is the same as multiplying by its reciprocal:
    x=12×32 x = \frac{1}{2} \times \frac{3}{2} .

  7. Simplify the multiplication:
    x=34 x = \frac{3}{4} .

Therefore, the value of the parameter x x is 34\frac{3}{4}.

Answer

34 \frac{3}{4}