Question

Help pls i need these to be finished by tomorrow, i'll give brainliest to whoever helps the best. 1st. (Try the numbers 31, 32, 33, 34 in the equation 4 × (x + 8) = 5x − 2 to test whether any of them is a solution. a. 31 is a solution. c. 33 is a solution. b. 34 is a solution. d. 32 is a solution.)


2nd. (Try the numbers 9, 10, 11, 12 in the equation 60 − 3 ⋅ z = 30

to test whether any of them is a solution.

a. 11 is a solution. c. 12 is a solution.

b. 10 is a solution. d. 9 is a solution.)

Answer 1

Part a: Option b. 34 is a solution.

Part b: Option b. 10 is a solution.

Explanation:

Part a: The equation is $4(x+8)=5x-2$

To find solution to the equation, we can solve for x.

$\begin{aligned}4 x+32 &=5 x-2 \\34 &=x\end{aligned}$

The solution is $x=34$

To test whether $x=34$ is a solution, let us substitute $x=34$ in the equation $4(x+8)=5x-2$, we get,

$\begin{aligned}4 x+32 &=5 x-2 \\4(34)+32 &=5(34)-2 \\136+32 &=170-2 \\168 &=168\end{aligned}$

Since, the values on both sides of the equation are equal, $x=34$ is the solution.

Part b: The equation is $60-3z=30$

To find solution to the equation, we can solve for z.

$\begin{aligned}60-3 z &=30 \\-3 z &=-30 \\z &=10\end{aligned}$

The solution is $z=10$

To test whether $z=10$ is a solution, let us substitute $z=10$ in the equation $60-3z=30$, we get,

$\begin{array}{r}{60-3 z=30} \\{60-3(10)=30} \\{60-30=30} \\{30=30}\end{array}$

Since, the values on both sides of the equation are equal, $z=10$ is the solution.