Solving Linear Equations
These are the methods used to solve linear equations:
1. Simplify the algebraic expressions in the equation.
2. Usually, simplify completely on each side individually before doing something
to both sides.
3. Add or subtract the same number from both sides of the equation.
4. Multiply or divide both sides of the equation by the same nonzero number.
Eq. 1. Exercises. Do the following problems. On at least two of them,
check the solution by
plugging it into the equation to see if it works. Answers are below.
1. Solve: 10x + 2x = 96
2. Solve: 2x + x = 72
3. Solve: 9x – 2x = 105
4. Solve: 112 = 6x – 2x
5. Solve: 3x = 9 * 4 – 12
6. Solve: 27 – 2*6 = 5x
In the following four problems, fill in the blank with either the word
“simplify” or “solve” to
indicate what instruction would usually be given for a problem like this. Then
follow the
instruction you just wrote and work the problem.
7. ______________ : 4*5 + 7*10
8. ______________ : 12 = 5x + x
9. ______________ : 4x + x
10. ______________ : 4*5 + 7*10 = 4x + x
Answers to Eq. 1:
1. x = 8
2. x = 24
3. x = 15
4. x = 28
5. x = 8
6. x = 3
7. “Simplify” 90
8. “Solve” x = 2
9. “Simplify” 5x
10. “Solve” x = 18
