Final answer:
The solution to the inequality 4 + 3/4(x + 2) < 3/8x + 1 is found by distributing, combining like terms, and dividing both sides by the coefficient of x to arrive at x < -9.3333.
Step-by-step explanation:
To solve the inequality 4 + 3/4(x + 2) < 3/8x + 1, we need to simplify and isolate the variable x. Let's first distribute the 3/4 to both terms inside the parentheses.
4 + (3/4)x + (3/4)*2 < (3/8)x + 1
4 + (3/4)x + 3/2 < (3/8)x + 1
Now, let's combine like terms by subtracting (3/8)x from both sides and subtracting 4 from both sides.
(3/4)x - (3/8)x < 1 - 4 - 3/2
To combine the x terms, we need a common denominator, which is 8 in this case:
(6/8)x - (3/8)x < -3.5
(3/8)x < -3.5
Now, divide both sides by (3/8) to solve for x:
x < -3.5 / (3/8)
x < -3.5 * (8/3)
x < -9.3333
The solution to the inequality is x < -9.3333.