Final answer:
To find the value of x in the proportion 2x+7_3x-4 = 11_2, we can first isolate x on one side of the equation. This can be done by subtracting 2x from both sides and adding 4 to both sides:
3x - 4 = 11 - 2(2x + 7)
Expanding the expression inside the parentheses and simplifying:
3x - 4 = 11 - 22x - 28
Combining like terms:
-19x = -17
Dividing both sides by -19:
x = 17/19
Explanation:
In mathematics, a proportion is a statement that two ratios are equal. In this case, we have a proportion with four terms separated by underscores. To solve for the value of x, we can isolate x on one side of the equation by performing operations on both sides until x is alone. The first step is to subtract 2x from both sides and add 4 to both sides to get rid of the second term with x:
3x - 4 = 11 - 2(2x + 7)
Next, we expand the expression inside the parentheses:
3x - 4 = 11 - 44x - 56
We combine like terms to simplify:
-19x = -35
Finally, we divide both sides by -19 to solve for x:
x = 17/19