Ask a New Question
Menu

What is the solution of the equation 8/9(x+1/2)=32/3 when solving for x ?(1 point)

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

To solve the equation 8/9(x+1/2) = 32/3 for x, we can start by multiplying both sides of the equation by 9/8 to eliminate the fraction on the left side:

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

The (8/9) and (9/8) cancel out, leaving:

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

Multiplying 32/3 by 9/8, we get:

x + 1/2 = 288/24

Reducing 288/24, we get:

x + 1/2 = 12/1

Now, to isolate x, we subtract 1/2 from both sides of the equation:

x = 12/1 - 1/2

To subtract these fractions, we need a common denominator of 2, so we can rewrite 12/1 as 24/2:

x = 24/2 - 1/2

Combining the fractions, we get:

x = 23/2

So, the solution to the equation is x = 23/2.

User Icon for Explain Bot Explain Bot answered
1 year ago

To find the solution for the equation (8/9)(x + 1/2) = 32/3, we need to isolate the variable x.

First, distribute the (8/9) to both terms inside the parenthesis:

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

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

Now simplify the expression: (8/9)(1/2) = 8/18 = 4/9

(8/9)x + 4/9 = 32/3

Next, subtract 4/9 from both sides of the equation to isolate the term with x:

(8/9)x = 32/3 - 4/9

To subtract fractions, we need to have a common denominator, which is 9:

(8/9)x = (32/3)(3/3) - (4/9)

(8/9)x = 96/9 - 4/9

Now, combine the fractions with the same denominator:

(8/9)x = (96 - 4)/9

(8/9)x = 92/9

Finally, to solve for x, divide both sides of the equation by 8/9:

(8/9)x / (8/9) = (92/9) / (8/9)

The (8/9) term in the numerator and denominator cancels out:

x = (92/9) / (8/9)

Now, dividing fractions is the same as multiplying by the reciprocal of the divisor:

x = (92/9) * (9/8)

Cross-cancel common factors if possible:

x = (23/2) * (1/1)

x = 23/2

Therefore, the solution to the equation (8/9)(x + 1/2) = 32/3 when solving for x is x = 23/2.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To solve the equation (8/9)(x + 1/2) = 32/3 for x, follow these steps:

Step 1: Distribute the 8/9 to the terms inside the parentheses:
(8/9)(x) + (8/9)(1/2) = 32/3

Simplified step:
(8/9)x + 4/9 = 32/3

Step 2: Simplify the equation by finding a common denominator for 9 in the fractions on the left side. Multiply the numerator and denominator of (8/9)x by 3 to obtain a common denominator:
(8/9)x + (4/9)(3/3) = 32/3

Simplified step:
(8/9)x + 12/9 = 32/3

Step 3: Combine like terms on the left side by adding the fractions:
(8/9)x + 12/9 = 32/3
(8/9)x + 4/3 = 32/3

Step 4: Set the equation equal to zero by subtracting 4/3 from both sides:
(8/9)x + 4/3 - 4/3 = 32/3 - 4/3
(8/9)x = 28/3

Step 5: Isolate x by multiplying both sides of the equation by the reciprocal of 8/9, which is 9/8:
(8/9)x * (9/8) = (28/3) * (9/8)
x = (252/24)

Step 6: Simplify the fraction if possible:
x = 10.5

Therefore, the solution to the equation (8/9)(x + 1/2) = 32/3 when solving for x is x = 10.5.