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

Answer 1

To solve the equation, let's simplify it step by step.

First, let's distribute the fraction 8/9 to the terms inside the parentheses:

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

Simplifying the fraction with a common denominator:

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

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

Now, let's clear the fraction by multiplying both sides of the equation by 2/8:

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

(1/4)(2x + 1) = 4/3

Next, distribute the (1/4) to the terms inside the parentheses:

(1/4)(2x) + (1/4)(1) = 4/3

(2/4)x + (1/4) = 4/3

Simplifying fractions and combining like terms:

(1/2)x + 1/4 = 4/3

Now, let's isolate the variable x by subtracting 1/4 from both sides of the equation:

(1/2)x + 1/4 - 1/4 = 4/3 - 1/4

(1/2)x = 4/3 - 1/4

Since the fractions have different denominators, we need to find a common denominator to subtract them. The least common denominator (LCD) is 12:

(1/2)x = 16/12 - 3/12

Now, we can subtract:

(1/2)x = 13/12

Finally, to solve for x, we multiply both sides of the equation by the reciprocal of 1/2, which is 2:

2 * (1/2)x = 2 * (13/12)

Multiplying the fractions and simplifying:

x = 26/12

Simplifying the fraction:

x = 13/6

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x is x = 13/6.

Answer 2

wrong i think you need an update

Answer 3

Apologies for the mistake. Let's solve the equation correctly.

The given equation is:
(8/9)(x + 1/2) = 32/3

To simplify, we can first cancel out the common factor of 8/9 on both sides by multiplying both sides by 9/8:
(9/8)(8/9)(x + 1/2) = (9/8)(32/3)
(x + 1/2) = 36/3
(x + 1/2) = 12

Next, we can isolate x by subtracting 1/2 from both sides:
x = 12 - 1/2
x = 24/2 - 1/2
x = 23/2

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