41y+21y+5−12=0
y=?
To solve the given linear equation, we will follow these steps:
- Step 1: Combine the terms involving y.
- Step 2: Simplify the constants on the right side of the equation.
- Step 3: Isolate y to find its value.
Let’s solve the equation 41y+21y+5−12=0.
Step 1: Combine the like terms that involve y.
The coefficients of y are 41 and 21. To combine them, we need a common denominator, which is 4. Therefore:
41y+21y=41y+42y=43y.
Step 2: Simplify the constants.
The equation now becomes 43y+5−12=0.
Combine the constants: 5−12=−7.
The equation simplifies to 43y−7=0.
Step 3: Isolate y.
Add 7 to both sides of the equation:
43y=7.
To solve for y, multiply both sides by the reciprocal of 43, which is 34:
y=7×34=328.
Convert the fraction to a mixed number: 328=9⋅3+1=9 remainder 1. Thus, 328=931.
Therefore, the value of y is 931.