# Linear Equations in One Variable

Linear equation in one variable is the equation with standard form color(purple)(mx+b=0).

m and b are some numbers and x is a variable.

Examples of linear equations are:

• 4x+2=0
• -2a-3=0
• 3/2 m-5/3=0

Using equivalence of equations, we can convert some other equations into the standard form:

• 2x=5 is equivalent to 2x-5=0 (subtract 5 from both sides of equation)
• 3/2x=5-2/3x becomes 13/6x-5=0 (move everything to the left and combine like terms)
• sqrt(2)x-5=x+2 becomes (sqrt(2)-1)x-7=0 (move everything to the left and combine like terms)
• 1/y=2 becomes -2y+1=0 (multiply both sides by y and move everything to the left)

Equation is linear, when it is written in standard form and variable is raised to the first power only.

Following are NOT linear equations:

• 2x^2+3=0 (variable raised to the second power)
• 2y-3=3/2y^2 (there is variable, raised to the second power)
• 1/y+y=2 (if we multiply both sides by y, then we will get 1+y^2=2y, which is not quadratic)

Exercise 1. Determine, whether 2x=-5 is linear and write it in standard form if it is.

Answer: yes; 2x+5=0.

Exercise 2. Determine, whether 1=2/3 a is linear and write it in standard form if it is.

Answer: yes; 2/3a-1=0.

Exercise 3. Determine, whether x^2=7 is linear and write it in standard form if it is.

Exercise 4. Determine, whether 1/x+5=x is linear and write it in standard form if it is.
Answer: no. Multiplying both sides by x gives 1+5x=x^2.
Exercise 5. Determine, whether 3/x=7/3 is linear and write it in standard form.
Answer: yes; 7/3x-3=0.