Question

Determine the number of solutions to the equation below.*
1 (3x – 7) = } (x+6) - 6

Answer 1

The equation simplifies to 3x - 7 = x, which further simplifies to 2x - 7 = 0. Solving for x, we find the only solution is x = 3.5. This solution is checked and considered reasonable.

Step-by-step explanation:

The equation given by the student, after correcting the typo appears to be 1(3x – 7) = (x+6) - 6. To solve this equation, we need to follow a systematic approach:

1. Simplify both sides of the equation by removing any unnecessary terms and combining like terms.
2. Move the variables to one side of the equation and the constants to the other side of the equation.
3. Solve for x to find the value or values that satisfy the equation.

Let's simplify the equation:

3x - 7 = x + 6 - 6

Now, combine like terms:

3x - 7 = x

Subtract x from both sides:

2x - 7 = 0

Finally, add 7 to both sides:

2x = 7

Divide both sides by 2:

x = 3.5

Checking this solution, it is reasonable since when substituted back into the original equation the left and right sides are equal.

Therefore, this equation has one solution, x = 3.5.