Solve the equation. Check your solution.

Question

-6y + 5 = 29y - 2

Answer 1

To solve the equation, we need to isolate the variable y on one side of the equation.

First, let's combine the like terms on both sides:

-6y + 5 = 29y - 2

To move the terms with y to one side, we can subtract 29y from both sides:

-6y - 29y + 5 = -2

Combining like terms on the left side, we have:

-35y + 5 = -2

Next, let's isolate the variable y. We can do this by subtracting 5 from both sides:

-35y + 5 - 5 = -2 - 5

Simplifying, we get:

-35y = -7

To solve for y, we can divide both sides of the equation by -35:

(-35y)/-35 = -7/-35

The -35's cancel out on the left side, giving us:

y = 1/5

Now, let's check our solution. We substitute y = 1/5 back into the original equation:

-6(1/5) + 5 = 29(1/5) - 2

Simplifying, we get:

-6/5 + 5 = 29/5 - 2

Common denominators are needed, so let's multiply the fractions by 5 to get rid of the denominators:

(-6/5)(5) + (5)(5) = (29/5)(5) - (2)(5)

Simplifying further:

-6 + 25 = 29 - 10

19 = 19

The equation is true when y = 1/5, which means our solution is correct.