Solve the equation.EXAMPLE 6Solve: −2(x − 5) + 10 = −3(x + 2) + xSolutionThe final equatio...

Solve the equation.

EXAMPLE 6

Solve: −2(x − 5) + 10 = −3(x + 2) + x

Solution

The final equation contains no variable terms, and there is no value for x that makes 20 = −6 a true equation. We conclude that there is no solution to this equation. In set notation, we can indicate that there is no solution with the empty set, { }, or use the empty set or null set symbol, ➢. In this chapter, we will simply write no solution.

EXAMPLE 7

Solve: 3(x − 4) = 3x − 12

Solution

The left side of the equation is now identical to the right side. Every real number may be substituted for x and a true statement will result. We arrive at the same conclusion if we continue.

Again, one side of the equation is identical to the other side. Thus, 3(x − 4) = 3x − 12 is an identity and all real numbers are solutions. In set notation, this is {all real numbers}.

4(3x + 2) = 12x + 8