Question

solve the equation. check your solution.

1. $12t - 8t = -52$
2. $-3.8g + 5 + 2.7g = 12.7$

Explanation:

Problem 34: \(12t - 8t = -52\)

Step1: Combine like terms

\(12t - 8t = (12 - 8)t = 4t\), so the equation becomes \(4t = -52\).

Step2: Solve for \(t\)

Divide both sides by 4: \(t = \frac{-52}{4} = -13\).

Step3: Check the solution

Substitute \(t = -13\) into the original equation:
Left side: \(12(-13) - 8(-13) = -156 + 104 = -52\).
Right side: \(-52\).
Since left side = right side, the solution is correct.

Problem 36: \(-3.8g + 5 + 2.7g = 12.7\)

Step1: Combine like terms

\(-3.8g + 2.7g = (-3.8 + 2.7)g = -1.1g\), so the equation becomes \(-1.1g + 5 = 12.7\).

Step2: Isolate the variable term

Subtract 5 from both sides: \(-1.1g = 12.7 - 5 = 7.7\).

Step3: Solve for \(g\)

Divide both sides by \(-1.1\): \(g = \frac{7.7}{-1.1} = -7\).

Step4: Check the solution

Substitute \(g = -7\) into the original equation:
Left side: \(-3.8(-7) + 5 + 2.7(-7) = 26.6 + 5 - 18.9 = 31.6 - 18.9 = 12.7\).
Right side: \(12.7\).
Since left side = right side, the solution is correct.

Answer:

s:

• For problem 34: \(t = -13\)
• For problem 36: \(g = -7\)