Question

What is the value of FH in terms of x if FG = 3x − 5, GH = x + 3, and FH = 2x + 3? Please provide the solution step by step, simplifying the answer as a proper fraction, mixed number, or integer.

Answer 1

To find the value of FH, we set up the equation 2x + 3 = 4x - 2 by combining FG + GH, and then solve for x, yielding x = 5/2 or 2.5.

Step-by-step explanation:

To find the value of FH in terms of x, we need to consider the relationship between FG, GH, and FH. According to the problem, FH is the sum of FG and GH. Therefore, we can write the equation FH = FG + GH. Substitutely the provided equations: FH = (3x - 5) + (x + 3). Combining like terms gives us FH = 4x - 2.

Now we are given that FH also equals 2x + 3. We can set up the equation 2x + 3 = 4x - 2 to find the value of x. Solving for x, we subtract 2x from both sides to get 3 = 2x - 2, and then add 2 to both sides to obtain 5 = 2x. Finally, dividing both sides by 2 gives us the solution x = 5/2 or 2.5 as a mixed number.