Question

Solve negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4 for y.

Infinite solutions
No solution
y = −14
y = 0

Answer 1

To solve the equation

\[
-5y + \frac{7}{3}y = -5 - \frac{8}{3}y - 4,
\]

let's first simplify both sides of the equation.

1. Start with the right-hand side:
\[
-5 - 4 = -9,
\]
so it becomes:
\[
-5y + \frac{7}{3}y = -9 - \frac{8}{3}y.
\]

2. Now rewrite the equation:
\[
-5y + \frac{7}{3}y + \frac{8}{3}y = -9.
\]

Combine the \(y\) terms on the left side. Begin by finding a common denominator to combine \(-5y\) with the fractional terms. The common denominator of 1 and 3 is 3, therefore:

\[
-5y = - \frac{15}{3}y.
\]

Now rewrite the left-hand side:
\[
-\frac{15}{3}y + \frac{7}{3}y + \frac{8}{3}y = -9.
\]

Combine the coefficients:
\[
\left(-\frac{15}{3} + \frac{7}{3} + \frac{8}{3}\right)y = -9,
\]
which simplifies to:
\[
\left(-\frac{15}{3} + \frac{15}{3}\right)y = -9.
\]

This results in:
\[
0y = -9.
\]

Since \(0y\) equals \(0\), we have:

\[
0 = -9,
\]

which is a contradiction. This indicates that there are no values of \(y\) that satisfy the equation.

Thus, the conclusion is that there is **no solution** for this equation.