Which of the following equations has a solution different from the rest?
Options:
-1/7x - 3/4 = 1/4
-0.35x - 0.52 = 1.93
3/4x + 5 = -1/4
1/2x - 3 = 1/2
To determine which equation has a different solution, we can solve each equation and see if the solution is different from the others.
1. -1/7x - 3/4 = 1/4
To begin solving this equation, we can start by isolating the variable x by moving the constants to the other side of the equation.
-1/7x = 1/4 + 3/4
-1/7x = 4/4
-1/7x = 1
To solve for x, we can multiply both sides of the equation by -7/1.
-7/1 * -1/7x = -7/1 * 1
x = -7
The solution for this equation is x = -7.
2. -0.35x - 0.52 = 1.93
Again, we can begin by isolating the variable x.
-0.35x = 1.93 + 0.52
-0.35x = 2.45
To solve for x, we divide both sides of the equation by -0.35.
-0.35x / -0.35 = 2.45 / -0.35
x = -7
The solution for this equation is x = -7.
3. 3/4x + 5 = -1/4
Following the same steps, we isolate the variable x.
3/4x = -1/4 - 5
3/4x = -1/4 - 20/4
3/4x = -21/4
To solve for x, we multiply both sides of the equation by 4/3.
4/3 * 3/4x = 4/3 * -21/4
x = -21/3
Simplifying, we get x = -7.
The solution for this equation is x = -7.
4. 1/2x - 3 = 1/2
We isolate the variable x.
1/2x = 1/2 + 3
1/2x = 1/2 + 6/2
1/2x = 7/2
To solve for x, we multiply both sides of the equation by 2/1.
2/1 * 1/2x = 2/1 * 7/2
x = 7/1
The solution for this equation is x = 7.
After solving all four equations, we see that the solutions for equations 1, 2, and 3 are all x = -7, while the solution for equation 4 is x = 7. Therefore, the equation that has a different solution from the rest is 1/2x - 3 = 1/2.