Question

question 9
solve and check the equation.
4(2y - 2)=7(y + 5)
enter answer

question 10
solve and check the equation.
-7y + 10=-1 - 10y
a {-\frac{11}{3}}
b {-\frac{17}{6}}

Explanation:

Step1: Expand both sides

Expand $4(2y - 2)$ to get $8y-8$, and expand $7(y + 5)$ to get $7y + 35$. So the equation becomes $8y-8=7y + 35$.

Step2: Isolate the variable term

Subtract $7y$ from both sides: $8y-7y-8=7y-7y + 35$, which simplifies to $y-8=35$.

Step3: Solve for y

Add 8 to both sides: $y-8 + 8=35+8$, so $y = 43$.

Step4: Check the solution for Question 9

Substitute $y = 43$ into the original equation:
Left - hand side: $4(2\times43-2)=4(86 - 2)=4\times84 = 336$.
Right - hand side: $7(43 + 5)=7\times48=336$.

Step5: Solve Question 10

Add $10y$ to both sides of $-7y + 10=-1-10y$: $-7y+10y + 10=-1-10y+10y$, which gives $3y + 10=-1$.
Subtract 10 from both sides: $3y+10 - 10=-1-10$, so $3y=-11$.
Divide both sides by 3: $y=-\frac{11}{3}$.

Step6: Check the solution for Question 10

Substitute $y =-\frac{11}{3}$ into the original equation:
Left - hand side: $-7\times(-\frac{11}{3})+10=\frac{77}{3}+10=\frac{77 + 30}{3}=\frac{107}{3}$.
Right - hand side: $-1-10\times(-\frac{11}{3})=-1+\frac{110}{3}=\frac{-3 + 110}{3}=\frac{107}{3}$.

Answer:

Question 9: $y = 43$
Question 10: A. $\{-\frac{11}{3}\}$