x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) − 6

9 answers

To solve the equation x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) - 6, we need to simplify both sides and solve for x.

Starting with the left side:

x(8 + 2) + 3 = x(10) + 3 = 10x + 3

Now, simplifying the right side:

2(5 + x) + 5(x + 1) - 6 = 10 + 2x + 5x + 5 - 6
= 10 + 2x + 5x - 1
= 7x + 9

Now, we have the equation:

10x + 3 = 7x + 9

To isolate x on one side, we subtract 7x from both sides:

10x - 7x + 3 = 7x - 7x + 9
3x + 3 = 9

Next, subtract 3 from both sides:

3x + 3 - 3 = 9 - 3
3x = 6

Finally, divide both sides by 3 to solve for x:

3x/3 = 6/3
x = 2

Therefore, the solution to the equation is x = 2.
Solve for x.

x + 0.60(15) = 0.80(x + 15)
Responses
A 9
B 12
C 13
D 15
Let's solve for x in the equation:

x + 0.60(15) = 0.80(x + 15)

First, simplify the equation:

x + 9 = 0.80x + 12

Next, subtract 0.80x from both sides:

x - 0.80x + 9 = 0.80x - 0.80x + 12

This simplifies to:

0.20x + 9 = 12

Next, subtract 9 from both sides:

0.20x + 9 - 9 = 12 - 9

This simplifies to:

0.20x = 3

Finally, divide both sides by 0.20 to solve for x:

(0.20x)/0.20 = 3/0.20

This simplifies to:

x = 15

Therefore, the solution to the equation is x = 15.
What is the value of x, when 10(x + 2) = 5(x + 8)?
Responses
A x = 1
B x = 2
C x = 4
D x = 56
E x = 2 & 2/3
Let's solve for x in the equation:

10(x + 2) = 5(x + 8)

First, distribute the 10 and the 5 on each side:

10x + 20 = 5x + 40

Next, subtract 5x from both sides:

10x - 5x + 20 = 5x - 5x + 40

This simplifies to:

5x + 20 = 40

Next, subtract 20 from both sides:

5x + 20 - 20 = 40 - 20

This simplifies to:

5x = 20

Finally, divide both sides by 5 to solve for x:

5x/5 = 20/5

This simplifies to:

x = 4

Therefore, the value of x is 4, so the correct answer is C.
Solve the equation for x.
2/5(2x − 12) = −28
Responses
A −18
B −29
C −32
D −9
Let's solve the equation for x:

2/5(2x - 12) = -28

First, distribute the 2/5 to each term inside the parentheses:

(2/5)(2x) - (2/5)(12) = -28

This simplifies to:

(4/5)x - 24/5 = -28

Now, we need to isolate x. To do this, we'll add 24/5 to both sides:

(4/5)x - 24/5 + 24/5 = -28 + 24/5

This simplifies to:

(4/5)x = -140/5 + 24/5

Now, we'll combine the fractions on the right side:

(4/5)x = -116/5

To solve for x, we'll multiply both sides by the reciprocal of 4/5, which is 5/4:

(5/4)(4/5)x = (5/4)(-116/5)

This simplifies to:

x = -580/20

Further simplifying the right side:

x = -29

The correct answer is B, x = -29.
In the inequality, what are all the possible values of x?

2(x + 12) − 16 ≤ 8
Responses
A x < 0
B x ≤ 0
C x ≥ 0
D x ≤ 1
Let's solve the inequality for x:

2(x + 12) - 16 ≤ 8

First, simplify the left side of the inequality:

2x + 24 - 16 ≤ 8

This simplifies to:

2x + 8 ≤ 8

Now, subtract 8 from both sides:

2x + 8 - 8 ≤ 8 - 8

This simplifies to:

2x ≤ 0

Next, divide both sides by 2 to solve for x:

2x/2 ≤ 0/2

This simplifies to:

x ≤ 0

Therefore, all possible values of x that satisfy the inequality are x ≤ 0. The correct answer is B.