Stuck Can anyone help me with these Math questions, I hate math?

When solving for x, show all operation steps followed by results of performing those operations (i.e., show that you are adding four to both sides, then on the next line show the result of that operation). When the line you’re typing is an equation, you should not start the line with an extra leading equals sign.

1. Name the property of real numbers illustrated below. Be specific with the naming (include “of addition” or “of multiplication,” if applicable).

7 + 13 = 13 + 7

2. Combine like terms:

7x2 + 9x – 4x2 – 2 + 6x – 2x2 + 8

3. Solve for x:

8x – 2 = -2x + 18

4. Solve for x:

2(2x – 5) + 1 = x – 8 – 5x

5. Solve for x:

(x – 7)/5 – 5/2 = (x + 9)/10

6. Translate to an algebra statement; do not solve:

Three times the difference of five and a twice a number yields the same result as the same number increased by four.

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1) 7 add 13 = 20

where 13 add 7 is 20

i.e. 20 = 20

2) 1stly, keep squared terms together-:

7x^2 - 4x^2 - 2x^2 = x^2

then do x terms-:

9x + 6x = 15x

then numbers-:

-2 +8 = 6

Re-join together-:

Answer-: x^2 + 15x + 6

3) 8x - 2 = -2x + 18

first add 2x to each side-:

10x - 2 = 18

then add 2 to each side-:

10x = 20

divide both sides by 10-:

x = 2 (answer)

4) 2(2x - 5)+1 = x - 8 - 5

multiply out brackets-:

4x - 10 + 1 = x - 8 - 5

add up like terms-:

4x - 9 = x - 13

add 9 to each side-:

4 x = x - 4

take x from each side-:

3x = -4

divide by 3-:

x = - 4/3

5) Right I'm not going to step by step this-:

(x - 7) / 5 - 5/2 = (x + 9) / 10

10(x - 7) - 50/2 = 5(x + 9)

10x - 70 - 25 = 5x + 45

10x - 95 = 5x + 45

5x = 140

x = 28 (answer)

6) Are you sure you have written this down correctly ???

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1. Commutative property of addition. In general, if a and b are arbitrary numbers or expressions, a + b = b + a.

2. Like terms are terms with the same "pattern" of numbers, letters, and exponents. In the expression below, there are three "types" of terms: just numbers, number * x, number * x^2.

7x^2 + 9x – 4x^2 – 2 + 6x – 2x^2 + 8 =

Rearranging terms, so like terms stick together:

7x^2 - 4x^2 - 2x^2 + 9x + 6x - 2 + 8 =

Adding like terms:

x^2 + 15x + 6

3. 8x - 2 = -2x + 18

The objective is to get just one x at the left side, and only numbers in the right side.

Adding a quantity to both sides of an equation does not change the solution, so

8x - 2 = -2x + 18

8x - 2 + 2x = -2x + 18 + 2x

10x - 2 = 0x + 18

10x - 2 = 18 (0*x = 0)

10x - 2 + 2 = 18 + 2

10x = 20

Dividing both sides of the equation by a non-zero number does not change the solution, so

10x/10 = 20/10

x = 2

4. I won't solve this one for you, just give a hint: 2(2x - 5) = 4x - 10, distributive property of multiplication over addition.

5. Again, I will give only a hint: multiply both sides by the LCM of the denominators, namely 10.

6. "Three times the difference of five and a twice a number yields the same result as the same number increased by four."

Let's parse this phrase, using parenthesis just like in an expression. With practice, you will be able to do all this without writing, just looking at the text. For now, let's go step-by-step.

"Three times [the difference of five and a twice a number] yields the same result as [the same number increased by four]."

"Three times [the difference of [five and a twice a number]] yields the same result as [the same number increased by four]."

"Three times [the difference of [five and [a twice a number]]] yields the same result as [the same number increased by four]."

"A number" and "the same number" are the same, as implied. Let's call the number x.

"Three times [the difference of [five and [twice x]]] yields the same result as [x increased by four]."

"Twice x" is 2x, "x increased by four" is x + 4.

"Three times [the difference of [5 and 2x]] yields the same result as [x + 4]."

"Difference" is subtraction, so

"Three times [5 - 2x] yields the same result as [x + 4]."

"Three times" is multiplication by 3, so

"3(5 - 2x) yields the same result as [x + 4]."

"yields the same result as" is just equality, so

3(5 - 2x) = x + 4
1. commutative in addition

2.

(7x2 - 4x2 - 2x2) + (9x + 6x) + (8 - 2)

(7 - 4 - 2)x2 + (9 + 6)x + 6

1x2 + 15x + 6

3.

8x - 2 = -2x +18

8x + 2x = 18 + 2 ==%26gt; add 2x and then add 2 to both side

10x = 20 ==%26gt; simple addition

x = 20/10 ==%26gt; divide both side with 10

x = 2 ==%26gt; simple division

4.

2(2x – 5) + 1 = x – 8 – 5x

(4x - 10) +1 = (x - 5x) - 8 ==%26gt; left side:multiply 2 with 2x and -5, right side is just a simple addition

4x - 9 = -4x - 8 ==%26gt; just another simple addition

8x = 1 ==%26gt; add 9 and 4x to both side

x = 1/8 ==%26gt; divide both side with 8

5. multiply both side with 10, the rest is similar to no.4

2(x-7) - 5x5 = x+9

2x - 14 - 25 = x + 9

2x -39 = x + 9

x = 48

6.

lets assume the number is x

"twice a number" means 2x

"difference of five and a twice a number" means 5 - 2x

"Three times the difference of five and a twice a number" means 3(5-2x)

"the same number increased by four" means x+4

so, we'll have

3(5-2x) = x + 4