3.2 If $$ a=-2, b=3 a-1, c=-4-b $$ and $$ x=3+c $$, determine the value of $$ x $$. 3.3 The sum of three consecutive integers are -75 . Calculate the value of the second integer.

Question

UpStudy AI · Accepted Answer

**Problem 3.2**

1. We are given:
   - $$ a = -2 $$
   - $$ b = 3a - 1 $$
   - $$ c = -4 - b $$
   - $$ x = 3 + c $$

2. Substitute $$ a $$ into the expression for $$ b $$:
   $$
   b = 3(-2) - 1 = -6 - 1 = -7
   $$

3. Substitute $$ b $$ into the expression for $$ c $$:
   $$
   c = -4 - (-7) = -4 + 7 = 3
   $$

4. Substitute $$ c $$ into the expression for $$ x $$:
   $$
   x = 3 + 3 = 6
   $$

Thus, the value of $$ x $$ is $$\boxed{6}$$.

---

**Problem 3.3**

1. Let the three consecutive integers be:
   $$
   n, \quad n+1, \quad n+2
   $$

2. Write the equation for their sum:
   $$
   n + (n+1) + (n+2) = 3n + 3
   $$

3. According to the problem, the sum is $$-75$$:
   $$
   3n + 3 = -75
   $$

4. Solve for $$ n $$:
   $$
   3n = -75 - 3 = -78
   $$
   $$
   n = \frac{-78}{3} = -26
   $$

5. The second integer is:
   $$
   n+1 = -26 + 1 = -25
   $$

Thus, the value of the second integer is $$\boxed{-25}$$.
**Problem 3.2** - $$ a = -2 $$ - $$ b = 3(-2) - 1 = -7 $$ - $$ c = -4 - (-7) = 3 $$ - $$ x = 3 + 3 = 6 $$ So, $$ x = 6 $$. **Problem 3.3** - Let the integers be $$ n $$, $$ n+1 $$, $$ n+2 $$ - Sum: $$ n + (n+1) + (n+2) = 3n + 3 = -75 $$ - Solve for $$ n $$: $$ 3n = -78 $$ ⇒ $$ n = -26 $$ - Second integer: $$ n+1 = -25 $$ Thus, the second integer is $$-25$$.

3.2 If \( a=-2, b=3 a-1, c=-4-b \) and \( x=3+c \), determine the value of \( x \). 3.3 The sum of three consecutive integers are -75 . Calculate the value of the second integer.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions