Final answer:
To solve the equation 1 2/3 x + 5/6 x = 30, you need to combine the terms on the left side of the equation. Convert the fractions into fractions with a common denominator, add the like terms, and solve for x.
Step-by-step explanation:
To solve the equation 1 2/3 x + 5/6 x = 30, you need to combine the terms on the left side of the equation. In this case, you have two fractions with different denominators. To add or subtract fractions, you need a common denominator. The least common multiple of 3 and 6 is 6. So, you need to convert the fractions into fractions with a denominator of 6. Multiplying the first fraction by 2/2 and the second fraction by 1/1 will give you:
2/3 x * 2/2 + 5/6 x * 1/1 = 30
4/6 x + 5/6 x = 30
Now, you can add the like terms on the left side of the equation:
(4/6 + 5/6) x = 30
Simplifying the fraction, you get:
9/6 x = 30
To solve for x, divide both sides of the equation by 9/6:
x = (30)/(9/6)
Dividing fractions is the same as multiplying by the reciprocal, so:
x = (30) * (6/9)
Calculating the multiplication, you get:
x = 180/9
Simplifying the fraction, you get:
x = 20