Question

aim: review of solving equations of the form $ax = b$ and $x + a = b$.
do now

1. add $(6k^2 - 5k - 4) + (k^2 - 6k + 2)$.
2. from $(t^2 + 3t - 5)$ subtract $(t^2 - 5t + 3)$.
3. find the solution to each equation.

a. $y - 7 = 12$
b. $9 = x + 8$
c. $x - 2.5 = 4$

1. find the solution of each equation.

a. $-6x = -12$
b. $4y = 8$
c. $\frac{a}{3} = -2$

Explanation:

Question 1

Step1: Combine like terms for \(k^2\)

\(6k^2 + k^2 = 7k^2\)

Step2: Combine like terms for \(k\)

\(-5k - 6k = -11k\)

Step3: Combine constant terms

\(-4 + 2 = -2\)

Step4: Write the result

\((6k^2 - 5k - 4)+(k^2 - 6k + 2)=7k^2 - 11k - 2\)

Step1: Distribute the subtraction

\((t^2 + 3t - 5)-(t^2 - 5t + 3)=t^2 + 3t - 5 - t^2 + 5t - 3\)

Step2: Combine like terms for \(t^2\)

\(t^2 - t^2 = 0\)

Step3: Combine like terms for \(t\)

\(3t + 5t = 8t\)

Step4: Combine constant terms

\(-5 - 3 = -8\)

Step5: Write the result

\((t^2 + 3t - 5)-(t^2 - 5t + 3)=8t - 8\)

Step1: Add 7 to both sides

\(y - 7 + 7 = 12 + 7\)

Step2: Simplify

\(y = 19\)

Answer:

\(7k^2 - 11k - 2\)

Question 2