Solve for ‘a’ in equation 6a-4=-2

Solve for ‘a’ in equation 6a-4=-2

Answer

a= 0.33333

The answer to the equation 6a – 4= -2 is 0.33333.

Solution

Reorder the terms:

-4 + 6a = -2

Solving

-4 + 6a = -2

Solving for variable ‘a’.

Move all terms containing a to the left, all other terms to the right.

Add ‘4’ to each side of the equation.

-4 + 4 + 6a = -2 + 4

Combine like terms: -4 + 4 = 0

0 + 6a = -2 + 4

6a = -2 + 4

Combine like terms: -2 + 4 = 2

6a = 2

Divide each side by ‘6’.

a = 0.33333

#Lesson on Equations

Equations in Mathematics: Definition, Types, Examples

An equation is a statement of equality between two expressions with the same value. It can also be defined as a pair of algebraic expressions with the same value, where one expression is an expansion or addition of the other. Equations are a fundamental component of any mathematical system because they allow us to express relationships between quantities and understand how they interact with each other.

Apart from this, they are used as a primary tool for problem-solving and proving things in mathematics. Again, we know that there are many types of equations. They can be classified into several broad categories based on their properties and usage. In this lesson, we shall learn about different kinds of equations and see some examples as well.

Parts of an Equation

The three parts of an equation are:

  1. Left Hand Side (LHS),
  2. Right Hand Side (RHS), and
  3. The equation sign.

Left Hand Side: This is the expression on the left side of the equation sign.

Right Hand Side: This is the expression on the right side of the equation sign.

Equation Sign: This is the equality sign between the two expressions to show that they have the same value.

How to Solve an Equation?

The best way to solve an equation is to isolate the variable by adding, subtracting, multiplying, or dividing both sides by certain numbers so that the equation becomes equal to zero. This means that both sides of the equation have the same value.

You can do this by using the following steps.

  • Solve for the Variable – First, isolate the variable by adding, subtracting, multiplying, or dividing both sides by some numbers.
  • Solve for the Unknown Quantity – Now that the variable has been isolated, you can solve for the unknown quantity in terms of the other terms in the equation.
  • Check the Result – Check whether the result obtained is the same on both sides of the equation. If yes, the equation has been solved. If not, go back to the first step and try again.

Types of Equations

We can classify equations into several broad categories based on their properties and usage.

  • Linear Equations
  • Quadratic Equations
  • Cubic Equations
  • Equations with unknown variables.

Linear Equations

These equations are those in which the variable appears only with a constant term. Linear equations can be written in the form of ax + b = c. Where a is the coefficient of x, b is the coefficient of y, and c is the constant term.

Linear equations can be classified into two types: linear homogeneous and linear inhomogeneous.

  • Linear homogeneous equations have the form ax + c = 0. They have a constant term along with a variable term and a zero term.
  • Linear inhomogeneous equations have the form ax + c = b. They have a constant term along with a variable term and a term that is not zero.

Quadratic Equations

The quadratic equation is one in which the variable appears only with a quadratic term. Quadratic equations can be written in the form of ax2 + bx + c = 0.

Quadratic equations can be classified into two types: quadratic homogeneous and quadratic inhomogeneous.

  • Quadratic homogeneous equations have the form ax2 + c = 0. They have a constant term along with a variable term and a zero term.
  • Quadratic inhomogeneous equations have the form ax2 + c > 0. They have a constant term along with a variable term and a term that is not zero.

Cubic Equations

Cubic equations are those in which the variable appears only with a cubic term. Cubic equations can be written in the form of ax3 + bx2 + cx + d = 0.

Cubic equations can be classified into two types: cubic homogeneous and cubic inhomogeneous.

  • Cubic homogeneous equations have the form ax3 + c = 0. They have a constant term along with a variable term and a zero term.
  • Cubic inhomogeneous equations have the form ax3 + c > 0. They have a constant term along with a variable term and a term that is not zero.

Equations with Unknown Variables

An equation with unknown variables is one in which both sides have variables, but none is specified. These kinds of equations can be solved using the techniques that we have discussed above for linear, quadratic, and cubic equations. To solve such equations, we need to first find the value of one of the variables present in the equation and then substitute it on the other side.

This can be done by using the following steps.

  • Solve for the Variable – First, isolate the variable by adding, subtracting, multiplying, or dividing both sides by some numbers.
  • Solve for the Unknown Quantity – Now that the variable has been isolated, you can solve for the unknown quantity in terms of the other terms in the equation.
  • Substitute the Value – Finally, substitute the value obtained in the other side of the equation.
  • Check the Result – Check whether the result obtained is the same on both sides of the equation. If yes, the equation has been solved. If not, go back to the first step and try again.

What is an Expression?

An expression can be described as an algebraic term that contains one or more numbers, variables, or both. The difference between an equation and an expression is that an equation is said to have two expressions that have the same value, whereas an expression can have any value.

Equations can be converted into expressions by multiplying or dividing both sides by the same non-zero number. Equations are related to expressions, but they are not the same. An equation is a specific kind of expression that has the same value.

Equation vs. Expression

An equation is a statement of equality between two expressions that have the same value. An expression can be any term, including an equation that has a value. An equation can be converted into an expression by multiplying both sides by a non-zero number. An expression can also be converted into an equation by multiplying both sides by the same non-zero number.

The main difference between an equation and an expression is that an equation has two expressions with the same value, and an expression can have any value.

Remark

This was all about different types of equations and their solution techniques. We hope that this lesson has helped you to understand equations better and how to solve them effectively.