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.
x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) − 6
9 answers
Solve for x.
x + 0.60(15) = 0.80(x + 15)
Responses
A 9
B 12
C 13
D 15
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.
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
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.
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
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.
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
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.
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.