Solve the Equation: 1/4y + 1/2y + 5 - 12 = 0

Question

14y+12y+512=0 \frac{1}{4}y+\frac{1}{2}y+5-12=0

y=? y=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 We want to isolate the unknown Y
00:08 Let's group terms
00:19 Multiply by the denominator to eliminate the fraction
00:33 Simplify as much as possible
00:38 Divide 4 by 2
00:47 Arrange the equation so that one side has only the unknown Y
00:54 Isolate the unknown Y
01:02 And this is the solution to the question

Step-by-Step Solution

To solve the given linear equation, we will follow these steps:

  • Step 1: Combine the terms involving y y .
  • Step 2: Simplify the constants on the right side of the equation.
  • Step 3: Isolate y y to find its value.

Let’s solve the equation 14y+12y+512=0 \frac{1}{4}y + \frac{1}{2}y + 5 - 12 = 0 .

Step 1: Combine the like terms that involve y y .
The coefficients of y y are 14 \frac{1}{4} and 12 \frac{1}{2} . To combine them, we need a common denominator, which is 4. Therefore:

14y+12y=14y+24y=34y \frac{1}{4}y + \frac{1}{2}y = \frac{1}{4}y + \frac{2}{4}y = \frac{3}{4}y .

Step 2: Simplify the constants.
The equation now becomes 34y+512=0 \frac{3}{4}y + 5 - 12 = 0 .
Combine the constants: 512=7 5 - 12 = -7 .

The equation simplifies to 34y7=0 \frac{3}{4}y - 7 = 0 .

Step 3: Isolate y y .
Add 7 to both sides of the equation:
34y=7 \frac{3}{4}y = 7 .

To solve for y y , multiply both sides by the reciprocal of 34 \frac{3}{4} , which is 43 \frac{4}{3} :

y=7×43=283 y = 7 \times \frac{4}{3} = \frac{28}{3} .

Convert the fraction to a mixed number: 283=93+1=9 remainder 1 \frac{28}{3} = 9 \cdot 3 + 1 = 9 \text{ remainder } 1. Thus, 283=913 \frac{28}{3} = 9\frac{1}{3} .

Therefore, the value of y y is 913 9\frac{1}{3} .

Answer

913 9\frac{1}{3}