Question

Find (x):

1. (0.15x + 6 = 51)
[ x = 51 - 6/0.15 ]

2. (-1.5x - 9 = 0)
[ x = -9/-1.5 ]

3. (1.3x = 54 + x)
[ x = 54/0.3 ]

4. (-0.7x + 2 = 65)
[ x = 2 - 65/-0.7 ]

5. ((x - 3) cdot 2 = 30)
[ x = 30/2 + 3 ]

6. (6x = -50)
[ x = -50/6 ]

7. (42x = 13 + 16x)
[ x = 13/26 ]

8. (2x + 9 = -x)
[ x = -9/3 ]

9. (5x - 4y = 24)

Answer 1

The student must use algebraic methods to solve equations for the variable x. This involves performing operations such as adding, subtracting, multiplying, dividing, and applying the quadratic formula to find the value of x.

Step-by-step explanation:

The student has presented a set of equations, and their goal appears to be to solve each for the variable x. Even though the question includes some incorrect solutions, to properly address the given problem, one must use algebraic methods to isolate x on one side of each equation.

Examples:

1. For the equation 0.15x + 6 = 51, subtract 6 from both sides to get 0.15x = 45, and then divide by 0.15 to find x.
2. For the equation -1.5x - 9 = 0, adding 9 to both sides gives -1.5x = 9, and then dividing by -1.5 will yield the value for x.
3. The quadratic equation x² +0.0211x -0.0211 = 0 can be solved using the quadratic formula, with a = 1, b = 0.0211, and c = -0.0211.

This approach will lead to finding the correct solutions for the variables x and potentially z and y, depending on the different equations provided.