Question

1.)Use the distributive property to write the next step in simplifying the equation. Use the asterisk symbol ( * ) to represent multiplication.

x(2 + 7) = 36

2.) Use the distributive property to write the next step in simplifying the equation. Use the asterisk symbol ( * ) to represent multiplication.

-1(4 + x) = 6

3.) Use the distributive property to write the next step in simplifying the variable expression. Use the asterisk symbol ( * ) to represent multiplication.

x(7 + 8)

Answer 1

1) x * 2 + x * 7 = 36

2) (-1) * 4 + (-1) * x = 6

3) x * 7 + x * 8

Explanation:

The distributive property states that when you multiply a number by the sum of two or more numbers, it is the same as multiplying the number by each of those numbers individually and then adding the results together.

In a simple form, it can be expressed as a * (b + c) = (a * b) + (a * c).

`\hrulefill`

Question 1

Given equation: x(2 + 7) = 36

Using the distributive property, the next step in simplifying the equation is:

`\large\textsf{x * 2 + x * 7 = 36}`

(The asterisk symbol ( * ) has been used to represent multiplication.)

`\hrulefill`

Question 2

Given equation: -1(4 + x) = 6

Using the distributive property, the next step in simplifying the equation is:

`\large\textsf{(-1) * 4 + (-1) * x = 6}`

(The asterisk symbol ( * ) has been used to represent multiplication.)

`\hrulefill`

Question 3

Given equation: x(7 + 8)

Using the distributive property, the next step in simplifying the equation is:

`\large\textsf{x * 7 + x * 8}`

(The asterisk symbol ( * ) has been used to represent multiplication.)

Answer 2

1) Next step: x * 2 + x * 7 = 36

2) Next step: - 1 * 4 - 1 * x = 6

3) Next step: x * 7 + x * 8

Explanation:

The distributive property is a mathematical property that states that multiplication distributes over addition and subtraction.

1.)

Distributive property:

`\sf a(b + c) = ab + ac`

x(2 + 7) = 36

Next step:

x * 2 + x * 7 = 36

Simplified:

2x + 7x = 36

9x = 36

`\sf x = (36)/(9)`

x = 4

2.)

Distributive property:

`\sf -a(b + c) = -ab - ac`

-1(4 + x) = 6

Next step:

- 1 * 4 - 1 * x = 6

Simplified:

-4 - x = 6

-x = 6+4

-x = 10

x = -10

3.)

Distributive property:

`\sf a(b + c) = ab + ac`

x(7 + 8)

Next step:

x * 7 + x * 8

Simplified:

7x + 8x

15x