Questionk) $5 g+34=-2(1-7 g)$ l) $12 t+8=\overline{3} t+71$ n) $-q-6=-10 q+57$ o) $3 c-5=-8(6+5 c)$

Studdy Solution
Isolate $g$ by dividing both sides by $-9$.
$$g = \frac{-36}{-9}$$
$$g = 4$$
**Solution for k: $g = 4$**
---
**Problem l: $12t + 8 = 3t + 71$**
STEP_1: Combine like terms by moving $t$ terms to one side and constants to the other side.
$$12t - 3t = 71 - 8$$
$$9t = 63$$
STEP_2: Isolate $t$ by dividing both sides by $9$.
$$t = \frac{63}{9}$$
$$t = 7$$
**Solution for l: $t = 7$**
---
**Problem n: $-q - 6 = -10q + 57$**
STEP_1: Combine like terms by moving $q$ terms to one side and constants to the other side.
$$-q + 10q = 57 + 6$$
$$9q = 63$$
STEP_2: Isolate $q$ by dividing both sides by $9$.
$$q = \frac{63}{9}$$
$$q = 7$$
**Solution for n: $q = 7$**
---
**Problem o: $3c - 5 = -8(6 + 5c)$**
STEP_1: Distribute $-8$ through the parentheses.
$$3c - 5 = -8 \cdot 6 + (-8) \cdot 5c$$
$$3c - 5 = -48 - 40c$$
STEP_2: Combine like terms by moving $c$ terms to one side and constants to the other side.
$$3c + 40c = -48 + 5$$
$$43c = -43$$
STEP_3: Isolate $c$ by dividing both sides by $43$.
$$c = \frac{-43}{43}$$
$$c = -1$$
**Solution for o: $c = -1$**
---
**Summary of Solutions:**
**k) $g = 4$**
**l) $t = 7$**
**n) $q = 7$**
**o) $c = -1$**