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

Answer 1

To solve the equation 8/9(x+1/2) = 32/3 for x, you can begin by simplifying the equation.

We can start by distributing the 8/9 to both terms inside the parentheses, which gives us:

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

Simplifying further, we have:

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

Next, we can subtract 4/9 from both sides of the equation:

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

Now, to combine the fractions on the right-hand side, we need to find a common denominator. The least common multiple of 3 and 9 is 9, so we can rewrite 32/3 as 96/9:

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

Simplifying the right-hand side, we have:

(8/9)x = 92/9

Finally, to solve for x, we can multiply both sides by the reciprocal of 8/9, which is 9/8:

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

x = 828/72

Simplifying the fraction, we get:

x = 23/2

Therefore, the solution for x is x = 23/2.