Doug C. answered • 09/02/23
Math Tutor with Reputation to make difficult concepts understandable
The left side of this equation has two terms which are +6y and -1.5x. The right side has one constant term.
A general strategy for solving linear equations for a particular variable (assuming there are not multiple fractions) is to simplify each side as much as possible by removing grouping symbols and combining similar terms (not necessary for the given equation). Then the idea is to get all terms containing the target variable on one side of the equal sign and all other terms on the other side of the equal sign. This is done using the addition and/or subtraction properties for equality. This step might also require combining similar terms. Finally divide both sides by the coefficient of the target variable (or multiply both sides by the reciprocal of the coefficient of the target variable. Yikes!
For the given equation:
6y -1.5x = 8, where the directions are to solve for y.
Use the addition property for equality to transpose the term -1.5x to the right side of the equal sign:
This is what you visualize:
6y - 1.5x + 1.5x = 8 + 1.5x, which results in:
6y = 8 +1.5x (another way to think about it: to transpose a term from one side of the equation, move it, but change its sign)
Since there are no similar terms to combine, ready for the final step which is to divide by sides by the coefficient of y (which is 6).
You might visualize this:
6y/6 = (8 + 1.5x)/6
But simply write this:
y = (8+1.5x)/6
Of course you can choose to divide 6 into both terms of the numerator and simplify:
y = 8/6 +1.5x/6
y = 4/3 + x/4
or
y = x/4 + 4/3
Visit this graph for confirmation:
desmos.com/calculator/4g8ccf0rsr
