## SOLVING LINEAR EQUATIONS

**
Recall the following:
**

**
**

** A linear equation is a polynomial of degree 1.
**

** In order to solve for the unknown variable, you must isolate the
variable
**

** In the order of operations, multiplication and division are completed
before addition and subtraction.
**

**Problem 1.1a:** *x* + 7 = 3

** Answer:** *x* = - 4

**Solution:** Subtract 7 from both sides of the equation.

which gives:

*x* = - 4

Check: Substitute -4 for *x* in the original equation. If, after the
substitution, the left side equals the right side, your answer is
correct. **( -4 ) + 7 = 3** Your answer is correct.

**Problem 1.1b:** *x* - 3 = 4

** Answer:** *x* = 7

**Solution:** Add 3 to both sides of the equation

which gives:

*x* = 7

Check: Substitute 7 for *x* in the original equation. If,
after the substitution, the left side equals the right side, your answer is correct. **( 7 ) - 3 = 4 **. Your answer is correct.

**Problem 1.1c:** *x* - 17 = 3

** Answer:** *x * = 20

**Solution:** Add 17 to both sides of the equation.

which gives:

*x * = 20

Check: Substitute **20** for *x* in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. **(20) - 17 = 3** . Your answer is correct.

**Problem 1.1d:** *x* + 5 = 8

**
**** Answer:** *x* = 3

**Solution:** Subtract 5 from both sides of the equation.

which gives:

*x * = 3

Check: Substitute **3** for *x* in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. **(3) + 5 = 8**. Your answer is correct.

**Problem 1.1e:**

** Answer:**

**Solution:** Add to both sides of the equation.

which gives:

Add the fractions.

Check: Substitute for *x* in the original equation. If, after the substitution, the left side equals the right side, your answer is correct.
.

Your answer is correct.

**If you would like to go back to the equation Table of contents, click on Contents**.

**
**

**
[Algebra]
[Trigonometry]
**** **
[Geometry]
[Differential Equations]
[Calculus]
[Complex Variables]
[Matrix Algebra]

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**Author:Nancy Marcus**

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