Answer :
Let's solve the two parts of the provided question step by step.
### Part A: Multiplication
We are asked to calculate the product of [tex]\((-8)\)[/tex] and [tex]\((-4)\)[/tex]:
[tex]\[ (-8) \cdot (-4) \][/tex]
When multiplying two negative numbers, the result is a positive number. Therefore, we get:
[tex]\[ (-8) \cdot (-4) = 32 \][/tex]
### Part B: Solving the Equation
We need to solve the following linear equation for [tex]\( x \)[/tex]:
[tex]\[ -31 \cdot x - 4 = 124 \][/tex]
Let's solve step by step:
1. Isolate the term containing [tex]\( x \)[/tex]:
[tex]\[ -31 \cdot x - 4 = 124 \][/tex]
Add 4 to both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ -31 \cdot x - 4 + 4 = 124 + 4 \][/tex]
[tex]\[ -31 \cdot x = 128 \][/tex]
2. Divide both sides by -31 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{128}{-31} \][/tex]
[tex]\[ x = -\frac{128}{31} \][/tex]
Thus, the solution to the equation is:
[tex]\[ x = -\frac{128}{31} \][/tex]
### Summary of Answers
- The product of [tex]\((-8) \cdot (-4)\)[/tex] is [tex]\( 32 \)[/tex].
- The solution to the equation [tex]\(-31 \cdot x - 4 = 124\)[/tex] is [tex]\( x = -\frac{128}{31} \)[/tex].
### Part A: Multiplication
We are asked to calculate the product of [tex]\((-8)\)[/tex] and [tex]\((-4)\)[/tex]:
[tex]\[ (-8) \cdot (-4) \][/tex]
When multiplying two negative numbers, the result is a positive number. Therefore, we get:
[tex]\[ (-8) \cdot (-4) = 32 \][/tex]
### Part B: Solving the Equation
We need to solve the following linear equation for [tex]\( x \)[/tex]:
[tex]\[ -31 \cdot x - 4 = 124 \][/tex]
Let's solve step by step:
1. Isolate the term containing [tex]\( x \)[/tex]:
[tex]\[ -31 \cdot x - 4 = 124 \][/tex]
Add 4 to both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ -31 \cdot x - 4 + 4 = 124 + 4 \][/tex]
[tex]\[ -31 \cdot x = 128 \][/tex]
2. Divide both sides by -31 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{128}{-31} \][/tex]
[tex]\[ x = -\frac{128}{31} \][/tex]
Thus, the solution to the equation is:
[tex]\[ x = -\frac{128}{31} \][/tex]
### Summary of Answers
- The product of [tex]\((-8) \cdot (-4)\)[/tex] is [tex]\( 32 \)[/tex].
- The solution to the equation [tex]\(-31 \cdot x - 4 = 124\)[/tex] is [tex]\( x = -\frac{128}{31} \)[/tex].
