Question

Solve the equation and check your solution:

1/3(9 - 2x) = x + 1

a) x = 3
b) x = -3
c) x = 2
d) x = -2

Answer 1

To solve the given equation, we simplify and isolate x by performing arithmetic operations using the distributive property and combining like terms. The solution is x = 6/5, which can be checked by substituting it back into the original equation.

Step-by-step explanation:

To solve the equation 1/3(9 - 2x) = x + 1, we need to simplify both sides and isolate x.

Multiplying both sides by 3 to get rid of the fraction, we have: 9 - 2x = 3(x + 1).

Distributing on the right side, we simplify the equation to: 9 - 2x = 3x + 3.

Combining like terms, we get: 9 = 5x + 3.

Subtracting 3 from both sides, we have: 6 = 5x.

Dividing both sides by 5, we find: x = 6/5.

Checking our solution, we substitute the value of x = 6/5 back into the original equation:

1/3(9 - 2(6/5)) = (6/5) + 1

Simplifying both sides, we get: 3 = 3. Since both sides are equal, our solution is correct.