Question

5/8 (x - 1/2) = 10

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing the fraction 5/8 to the terms inside the parentheses:
(5/8)(x) - (5/8)(1/2) = 10

Simplifying this expression, we get:
(5/8)x - 5/16 = 10

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
(5/8)x = 10 + 5/16

Simplifying the right-hand side:
(5/8)x = 160/16 + 5/16
(5/8)x = 165/16

3. To eliminate the fraction, multiply both sides of the equation by the reciprocal of 5/8, which is 8/5:
(8/5)(5/8)x = (8/5)(165/16)

Simplifying this expression:
x = (8/5)(165/16)
x = (8 * 165) / (5 * 16)

4. Lastly, simplify the expression to get the final answer for x:
x = 1320/80
x = 33/2
x = 16.5

Therefore, the solution to the equation 5/8 (x - 1/2) = 10 is x = 16.5.

Answer 2

[AI-generated answer — Explain Bot]

To solve the equation 5/8(x - 1/2) = 10, we can follow these steps:

Step 1: Distribute the fraction 5/8 to the terms inside the parentheses:
(5/8)(x) - (5/8)(1/2) = 10

Step 2: Simplify the expression by multiplying the fractions:
(5/8)x - 5/16 = 10

Step 3: To eliminate the fraction, we can multiply the entire equation by the least common denominator (LCD) of the fractions, which is 16. This will result in a more straightforward equation:
16 * (5/8)x - 16 * (5/16) = 16 * 10
(80/8)x - 5 = 160

Step 4: Simplify the equation further:
10x - 5 = 160

Step 5: Now, we can solve for x. Start by isolating the variable x. Add 5 to both sides of the equation:
10x - 5 + 5 = 160 + 5
10x = 165

Step 6: Divide both sides of the equation by 10 to solve for x:
10x/10 = 165/10
x = 16.5

So, the solution to the equation 5/8(x - 1/2) = 10 is x = 16.5.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To solve the equation 5/8 (x - 1/2) = 10, we can follow these steps:

Step 1: Distribute the 5/8 to the terms inside the parentheses:
(5/8) * (x) - (5/8) * (1/2) = 10

Simplifying, we have:
(5/8)x - 5/16 = 10

Step 2: Add 5/16 to both sides of the equation to isolate the variable term:
(5/8)x = 10 + 5/16

Simplifying, we have:
(5/8)x = 161/16

Step 3: Multiply both sides of the equation by the reciprocal of 5/8, which is 8/5, to solve for x:
((8/5) * (5/8))x = (8/5) * (161/16)

Simplifying, we have:
x = 1288/80

Step 4: Simplify the fraction on the right-hand side:
x = 16.1

Therefore, the value of x that satisfies the equation 5/8 (x - 1/2) = 10 is x = 16.1.

Answer 4

4.72 (x - 6.56) = 10.4

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing 4.72 to the terms inside the parentheses:
4.72x - 4.72 * 6.56 = 10.4

Simplifying the expression, we get:
4.72x - 30.8992 = 10.4

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
4.72x = 10.4 + 30.8992

Simplifying the right-hand side:
4.72x = 41.2992

3. To solve for x, divide both sides of the equation by 4.72:
(4.72x) / 4.72 = (41.2992) / 4.72

Simplifying the expression:
x = 8.75

Therefore, the solution to the equation 4.72(x - 6.56) = 10.4 is x = 8.75.

Answer 6

8/9 (x + 1/2) = 32/3

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing the fraction 8/9 to the terms inside the parentheses:
(8/9)(x) + (8/9)(1/2) = 32/3

Simplifying this expression, we get:
(8/9)x + 4/9 = 32/3

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
(8/9)x = 32/3 - 4/9

Simplifying the right-hand side:
(8/9)x = (96/9) - (4/9)
(8/9)x = 92/9

3. To eliminate the fraction, multiply both sides of the equation by the reciprocal of 8/9, which is 9/8:
(9/8)(8/9)x = (9/8)(92/9)

Simplifying this expression:
x = (9/8)(92/9)
x = (9 * 92) / (8 * 9)

4. Lastly, simplify the expression to get the final answer for x:
x = 828/72
x = 23/2
x = 11.5

Therefore, the solution to the equation 8/9 (x + 1/2) = 32/3 is x = 11.5.

Answer 8

6.24 (x + 5.9) = 20.22

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing 6.24 to the terms inside the parentheses:
6.24x + 6.24 * 5.9 = 20.22

Simplifying the expression, we get:
6.24x + 36.816 = 20.22

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
6.24x = 20.22 - 36.816

Simplifying the right-hand side:
6.24x = -16.596

3. To solve for x, divide both sides of the equation by 6.24:
(6.24x) / 6.24 = (-16.596) / 6.24

Simplifying the expression:
x = -2.66

Therefore, the solution to the equation 6.24 (x + 5.9) = 20.22 is x = -2.66.

Answer 10

82.78 (p = 11.892) = 72.8464

Answer 11

[AI-generated answer — Bot GPT 3.5]

Apologies, but it seems like there is a mistake in the equation you provided. It should be:

82.78 (p + 11.892) = 72.8464

To solve this equation, we can follow these steps:

1. Begin by distributing 82.78 to the terms inside the parentheses:
82.78p + 82.78 * 11.892 = 72.8464

Simplifying the expression, we get:
82.78p + 982.67016 = 72.8464

2. Next, isolate the term with p on one side of the equation by moving the constant term to the other side:
82.78p = 72.8464 - 982.67016

Simplifying the right-hand side:
82.78p = -909.82376

3. To solve for p, divide both sides of the equation by 82.78:
(82.78p) / 82.78 = (-909.82376) / 82.78

Simplifying the expression:
p = -10.9996

Therefore, the solution to the equation 82.78 (p + 11.892) = 72.8464 is p = -10.9996.

Answer 12

5.6 (x + 1.42) = 7.8

Answer 13

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing 5.6 to the terms inside the parentheses:
5.6x + 5.6 * 1.42 = 7.8

Simplifying the expression, we get:
5.6x + 7.952 = 7.8

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
5.6x = 7.8 - 7.952

Simplifying the right-hand side:
5.6x = -0.152

3. To solve for x, divide both sides of the equation by 5.6:
(5.6x) / 5.6 = (-0.152) / 5.6

Simplifying the expression:
x = -0.027

Therefore, the solution to the equation 5.6 (x + 1.42) = 7.8 is x = -0.027.

Answer 14

9.8 (x - 2.14) = 53.9

Answer 15

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing 9.8 to the terms inside the parentheses:
9.8x - 9.8 * 2.14 = 53.9

Simplifying the expression, we get:
9.8x - 20.892 = 53.9

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
9.8x = 53.9 + 20.892

Simplifying the right-hand side:
9.8x = 74.792

3. To solve for x, divide both sides of the equation by 9.8:
(9.8x) / 9.8 = (74.792) / 9.8

Simplifying the expression:
x = 7.626

Therefore, the solution to the equation 9.8 (x - 2.14) = 53.9 is x = 7.626.

Answer 16

102.5 (x - 11.92) = 71.6

Answer 17

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing 102.5 to the terms inside the parentheses:
102.5x - 102.5 * 11.92 = 71.6

Simplifying the expression, we get:
102.5x - 1221.8 = 71.6

2. Next, isolate the term with x on one side of the equation by moving the constant term to the other side:
102.5x = 71.6 + 1221.8

Simplifying the right-hand side:
102.5x = 1293.4

3. To solve for x, divide both sides of the equation by 102.5:
(102.5x) / 102.5 = (1293.4) / 102.5

Simplifying the expression:
x = 12.636585365853658

Therefore, the solution to the equation 102.5 (x - 11.92) = 71.6 is x = 12.6366 (rounded to four decimal places).

Answer 18

50.3 (n + 9.25) = -120.72

Answer 19

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we can follow these steps:

1. Begin by distributing 50.3 to the terms inside the parentheses:
50.3n + 50.3 * 9.25 = -120.72

Simplifying the expression, we get:
50.3n + 464.275 = -120.72

2. Next, isolate the term with n on one side of the equation by moving the constant term to the other side:
50.3n = -120.72 - 464.275

Simplifying the right-hand side:
50.3n = -584.995

3. To solve for n, divide both sides of the equation by 50.3:
(50.3n) / 50.3 = (-584.995) / 50.3

Simplifying the expression:
n = -11.624326626438

Therefore, the solution to the equation 50.3 (n + 9.25) = -120.72 is n = -11.6243 (rounded to four decimal places).