Final answer:
To solve the equation (3/4)x + 3 = (7/10) for x, subtract 3 from both sides, convert to fractions, and then multiply by the reciprocal of (3/4). Simplify the resultant fraction to get x = -46/15.
Step-by-step explanation:
To solve the equation (3/4)x + 3 = (7/10) for x, we should first isolate the variable x on one side of the equation. We can subtract 3 from both sides of the equation to get (3/4)x = (7/10) - 3. Since we are instructed not to use decimals in the answer, it is best to work with fractions.
First, convert 3 to a fraction with a denominator of 10 to match the right side of the equation: 3 = 30/10. Now our equation looks like this:
(3/4)x = (7/10) - (30/10)
Next, subtract the fractions on the right side of the equation:
(3/4)x = -23/10
Now, to solve for x, multiply both sides by the reciprocal of (3/4), which is (4/3):
x = (-23/10) * (4/3)
When we multiply the fractions, we get:
x = -92/30
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
x = (-92/2) / (30/2)
x = -46/15