Solving Linear Equations

Introduction:

A linear equation in one variable is an equation of degree 1.

Example 1: 2x – 3 equals 12.

To solve a linear equation means to find the x-intercept of the line 2x- 3 equals 12. This is also known as the root of the equation. To check the answer simply substitute the root into the equation. And see if it makes the left side equal to the right side.

Example 2: Solve and check 2x – 3 equals 12.
Solution 2: 2x-3 plus 3 equals 12 plus 3. 2x equals 15.. 2x/2 equals 15/2. x equals 7’5. Check.2(7.5) – 3 equals 15-3 equals 12.

Example 3: Find the root of the equation: x-1/x-3 equals 4/5.
Solution 3: 5(x-1) equals 4(x-3). 5x-5 equals 4x-12. 5x-4x -5 plus 12 equals x plus 7 equals 0. The root is -7. Check: -8/-10 equals 4/5.

Example 4: solve 4(x- 1) -3(2x-5) equals 14.
Solution 4: 4x-4 -6x plus 15 equals 14. -2x plus 11 equals 14. -2x equals 3. X equals -3/2.