Question

Start Fraction 8 plus x over 2 End Fraction minus Start Fraction x plus 3 over 3 End Fraction equals 4
x equals negative 14
x = 6
x = 14
x equals negative 6

Answer 1

To solve the equation, we substitute the value of x into the equation and check if it balances.

For x = -14:
Start Fraction 8 plus (-14) over 2 End Fraction minus Start Fraction (-14) plus 3 over 3 End Fraction equals 4

Simplifying the equation:
Start Fraction 8 + (-14) over 2 End Fraction - Start Fraction (-14) + 3 over 3 End Fraction = 4
Start Fraction -6 over 2 End Fraction - Start Fraction -11 over 3 End Fraction = 4
-3 - (-11/3) = 4
-3 + 11/3 = 4
-9/3 + 11/3 = 4
(2/3) = 4

The equation does not balance for x = -14.

For x = 6:
Start Fraction 8 plus 6 over 2 End Fraction minus Start Fraction 6 plus 3 over 3 End Fraction equals 4

Simplifying the equation:
Start Fraction 8 + 6 over 2 End Fraction - Start Fraction 6 + 3 over 3 End Fraction = 4
14/2 - 9/3 = 4
7 - 3 = 4
4 = 4

The equation balances for x = 6.

For x = 14:
Start Fraction 8 plus 14 over 2 End Fraction minus Start Fraction 14 plus 3 over 3 End Fraction equals 4

Simplifying the equation:
Start Fraction 8 + 14 over 2 End Fraction - Start Fraction 14 + 3 over 3 End Fraction = 4
22/2 - 17/3 = 4
11 - 17/3 = 4
11 - 51/3 = 4
33/3 - 51/3 = 4
-18/3 = 4
-6 = 4

The equation does not balance for x = 14.

For x = -6:
Start Fraction 8 plus (-6) over 2 End Fraction minus Start Fraction (-6) plus 3 over 3 End Fraction equals 4

Simplifying the equation:
Start Fraction 8 + (-6) over 2 End Fraction - Start Fraction (-6) + 3 over 3 End Fraction = 4
2 - (-3/3) = 4
2 + 1 = 4
3 = 4

The equation does not balance for x = -6.

So, x = 6 is the only value that satisfies the equation.