Solve the equation using the addition property of equality. Be sure to check your proposed solution. $$ -3 y+7=-4 y+1 $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ -3y + 7 = -4y + 1 $$ using the addition property of equality, we will follow these steps:

1. **Isolate the variable $$ y $$**: We can do this by adding $$ 4y $$ to both sides of the equation to eliminate $$ -4y $$ from the right side.

$$
   -3y + 4y + 7 = 1
   $$

This simplifies to:

$$
   y + 7 = 1
   $$

2. **Continue isolating $$ y $$**: Next, we will subtract $$ 7 $$ from both sides to isolate $$ y $$.

$$
   y + 7 - 7 = 1 - 7
   $$

This simplifies to:

$$
   y = -6
   $$

3. **Check the proposed solution**: We will substitute $$ y = -6 $$ back into the original equation to verify if it holds true.

Original equation:

$$
   -3(-6) + 7 = -4(-6) + 1
   $$

Calculating both sides:

Left side:

$$
   -3(-6) + 7 = 18 + 7 = 25
   $$

Right side:

$$
   -4(-6) + 1 = 24 + 1 = 25
   $$

Since both sides are equal, the proposed solution $$ y = -6 $$ is correct.

Thus, the solution to the equation $$ -3y + 7 = -4y + 1 $$ is

$$
\boxed{-6}
$$
$$ y = -6 $$

Solve the equation using the addition property of equality. Be sure to check your proposed solution. \( -3 y+7=-4 y+1 \)