a Determine the value of x that will make both sides of the equation equal.
B
b Simplify the right-hand side of the equation. Then, determine the values of x that make both sides of the equation equal.
C
c Isolate x.
D
d Isolate x.
A
a x=0
B
b All real numbers.
C
c x=14
D
d No solutions.
Practice makes perfect
a Finding the value of x that makes the given equation true means finding the value that makes both sides of the equation equal.
x+5=5
Notice that the right-hand side of the equation is 5, while the left-hand side is the sum of 5 and an unknown number x. For the left-hand side of the equation to be equal to 5, x must be equal to 0. If x was different from 0, x+5 would not be equal to 5.
0+5=5
The only value of x that makes the equation true is 0.
b To determine the value of the variable x that makes the statement true, we should first simplify the right-hand side by combining like terms.
Notice that both sides of the equations are now the same expression. Therefore, no matter what value of x we substitute into the equation, the statement will always be true. This means that the all real numbers make the equation true.
c To determine the value of the variable that makes the equation true, we should isolate the variable on one side of the equation.
We got a false statement, since -1 can never be equal to 7. This means there are no values of x that will make the statement true. This equation has no solutions.
