complete the equation below to create an equation with no solution
5(4x+7)-2x=___x+21
a. 20
b. -20
c. 18
d. -18
The equation with no solution must result in a contradiction. To create a contradiction, we need to eliminate the variable "x" on one side of the equation.
Let's start by distributing 5 to both terms within the parentheses:
20x + 35 - 2x = ___x + 21
Combining like terms on the left side:
18x + 35 = ____x + 21
To eliminate the variable "x" on one side, we subtract "18x" from both sides:
35 = ____x + 21 - 18x
Combining like terms on the right side:
35 = ____x - 17x + 21
Now, subtract 21 from both sides:
14 = ____x - 17x
Rearrange the equation:
14 = -3x
Therefore, the equation with no solution is:
5(4x+7)-2x = -3x + 21.
The correct answer is (d) -18.