solve 1.2y + 7.8 = 0.4y + 15.4. enter your numerical answer below. question 7 solve: $\frac{2}{3}(12 - 6y)=2…

Explanation:

Step1: Isolate variable terms

Subtract $0.4y$ from both sides of $1.2y + 7.8=0.4y + 15.4$: $1.2y-0.4y + 7.8=0.4y-0.4y + 15.4$, which simplifies to $0.8y+7.8 = 15.4$.

Step2: Isolate the term with the variable

Subtract $7.8$ from both sides: $0.8y+7.8 - 7.8=15.4 - 7.8$, so $0.8y=7.6$.

Step3: Solve for $y$

Divide both sides by $0.8$: $y=\frac{7.6}{0.8}=\frac{76}{8} = 9.5$.

Step4: Solve the second - equation

First, distribute $\frac{2}{3}$ in $\frac{2}{3}(12 - 6y)=2 - 2y$. $\frac{2}{3}\times12-\frac{2}{3}\times6y=2 - 2y$, which is $8 - 4y=2 - 2y$.

Step5: Isolate variable terms

Add $4y$ to both sides: $8 - 4y+4y=2 - 2y+4y$, so $8=2 + 2y$.

Step6: Isolate the term with the variable

Subtract $2$ from both sides: $8 - 2=2 - 2+2y$, so $6 = 2y$.

Step7: Solve for $y$

Divide both sides by $2$: $y = 3$.

Answer:

For the first equation: $y = 9.5$ For the second equation: $y = 3$