Question

AQRS = ATUV RS = 6X-8 UV = 4x+2

Write and solve an equation to find the alue of x (must show work).

Answer 1

To find the value of x when AQRS equals ATUV, we equate RS (6x-8) to UV (4x+2) and solve the resulting equation 6x - 8 = 4x + 2, which gives us x = 5. Substituting x back confirms the solution is correct, as RS and UV are equal when x is 5.

Step-by-step explanation:

The question involves setting up and solving a linear equation. We are given two expressions: RS which is 6X-8 and UV which is 4x+2. Since AQRS equals ATUV, we set RS equal to UV to find the value of x:

6x - 8 = 4x + 2.

To solve for x, follow these steps:

1. Subtract 4x from both sides: 2x - 8 = 2.
2. Add 8 to both sides: 2x = 10.
3. Divide both sides by 2 to isolate x: x = 5.

To verify if the solution makes sense, substitute x back into the original expressions: RS = 6(5) - 8 = 30 - 8 = 22 and UV = 4(5) + 2 = 20 + 2 = 22, which confirms that RS equals UV when x is 5, fulfilling the condition AQRS = ATUV.