Question
Substitute the value of x back into the equation x + 3 – 2x = negative 2 x equals negative StartFraction one-fourth EndFraction plus StartFraction one-half EndFraction x plus 5. + x + 5 to justify the solution. What value of x is the solution?
x = ____
Answers
GPT 3.5
First, we substitute x = -1/4 + 1/2 into the equation given:
-1/4 + 1/2 + 3 - 2(-1/4 + 1/2) = -2(-1/4 + 1/2) + 5
-1/4 + 1/2 + 3 + 1/2 = 1/2 + 1 - 2(1/4) + 5
-1/4 + 1/2 + 3 + 1/2 = 1/2 + 1 - 1/2 + 5
-1/4 + 1/2 + 3 + 1/2 = 1/2 + 1/2 + 5
1/4 + 3 + 1/2 = 1 + 5
2.75 = 6
This equation is not true, so the value of x = -1/4 + 1/2 is not the solution.
Therefore, the correct value of x that is the solution to the equation x + 3 - 2x = -2x + 5 is:
x = -1/4 + 1/2 = 1/4
-1/4 + 1/2 + 3 - 2(-1/4 + 1/2) = -2(-1/4 + 1/2) + 5
-1/4 + 1/2 + 3 + 1/2 = 1/2 + 1 - 2(1/4) + 5
-1/4 + 1/2 + 3 + 1/2 = 1/2 + 1 - 1/2 + 5
-1/4 + 1/2 + 3 + 1/2 = 1/2 + 1/2 + 5
1/4 + 3 + 1/2 = 1 + 5
2.75 = 6
This equation is not true, so the value of x = -1/4 + 1/2 is not the solution.
Therefore, the correct value of x that is the solution to the equation x + 3 - 2x = -2x + 5 is:
x = -1/4 + 1/2 = 1/4