Algebra Know-It-ALL

194 First-Degree Equations in One Variable

Are you confused?

If you aren’t sure how the five solutions come out of the five original equations above, Tables 12-1 through

12-5 show the processes in each case, step-by-step in detail. The processes shown here don’t necessarily

represent the only ways the equations can be solved. Nevertheless, the solution to any equation should

always turn out the same, regardless of the sequence of steps. You might want to try solving some of these

equations in two or three different ways.

Table 12-1. Process for solving the equation x− 4 = 0.

Statements Reasons

x− 4 = 0 This is the equation we are given

x− 4 + 4 = 0 + 4 Add 4 to each side

x= 4 Simplify each side

Table 12-2. Process for solving the equation x+ 7 =−2.

Statements Reasons

x+ 7 =− 2 This is the equation we are given

x+ 7 − 7 =− 2 − 7 Subtract 7 from each side

x=− 9 Simplify each side

Table 12-3. Process for solving the equation a−x= 0.

Statements Reasons

a−x= 0 This is the equation we are given

−x=−a Subtract a from each side

−1(−x)=−1(−a) Multiply each side by − 1

x=a Simplify each side

Table 12-4. Process for solving the equation a− 5 +x= 0.

Statements Reasons

a− 5 +x= 0 This is the equation we are given

a− 5 +x−a= 0 −a Subtract a from each side

− 5 +x=−a Simplify each side

− 5 +x+ 5 =−a+ 5 Add 5 to each side

x= 5 −a Simplify each side