Question Video: Solving Linear Equations with the Unknown on Both Sides of the Equation Mathematics

Video Transcript

Find the solution set of the equation 41𝑎 divided by two equals seven plus three 𝑎.

In order to find the solution set or the value of 𝑎 that satisfies the equation, we’re going to use the balancing method. Multiplying both sides of the equation by two gives us 41𝑎 is equal to two multiplied by seven plus three 𝑎.

Expanding the bracket or parenthesis using the distributive method of multiplication gives us 14 plus six 𝑎, as two multiplied by seven is 14 and two multiplied by three 𝑎 is six 𝑎.

If we subtract six 𝑎 from both sides of this new equation, we are left with 35𝑎 equals 14. Finally, dividing both sides by 35 give us a value of 𝑎 of 14 over 35 or 14 35ths.

This fraction can be simplified by dividing the top, the numerator, and the bottom, the denominator, by seven. Dividing 14 by seven gives us two. And dividing 35 by seven gives us five. Therefore, 𝑎 is equal to two-fifths.

We could also write our answer as a decimal. Two-fifths is equal to 0.4. So 𝑎 could also be equal to 0.4. Therefore, the solution set to the equation 41𝑎 divided by two equals seven plus three 𝑎 is 0.4. The only value that solves the equation is 𝑎 equals 0.4.