Solve Equations

• Equations are numerical expressions containing an equal sign.
• An equation signifies \(2\) things are equivalent. The general structure of a linear equation in a variable is \(Ax + B = 0\). It’ll have the equals sign “\(=\)”. That equation states: what’s on the left \(Ax + B\) is equivalent to what’s on the right \((0)\). Therefore, equations are like a statement saying “this is equal to that”. Here the \(A\) is the coefficient of \(x\), and \(x\) is the variable, while \(B\) is the constant term. The coefficient, as well as the constant term, must be segregated to get the final result of the linear equation.
• Equations many times contain algebra. Algebra is utilized in Maths whenever we don’t know the correct numeral in a calculation – that unidentified value can be swapped with a letter.
• You get the answer to equations via figuring out the value for one letter. To resolve the equation you utilize the inverse operations to undo it.

Related Topics

• How to Solve One-Step Equations?
• How to Solve Multi-Step Equations?
• How to Solve Radical Equations?
• How to Solve Absolute Value Equations?

Right now, let’s find out the way to resolve a \(1\)-variable linear equation. 

• Step-one: Keep your variable term on one side, then put the constants on the other side of the equation via subtracting or adding on both sides of this equation.
• Step-two:  Make the constant terms simpler.
• Step-three: Set apart the variable on one side via multiplying or dividing it into both sides of your equation.
• Step-four: Simplify, then write down your results.

Crucial Notes

The subsequent points assist us in plainly summarizing all the concepts involved with linear equations in one variable.

• The variable’s degree in a linear equation ought to be precisely equal to one.
• A straight line signifies the graph for a linear equation, either a horizontal line or a vertical one.
• The resolution of a linear equation in one variable isn’t affected if any numeral is multiplied, subtracted or added, on both of the sides of your equation.

Solve Equations – Example 1:

Solve the equation.

\(12+x=20\)

Solution:

\(12+x=20\) is a linear equation having a single variable in it. Here, the operation is addition and its inverse operation is subtraction. To solve this equation, subtract \(12\) from both sides of the equation: \(12+x=20→12+x−12=20-12 \).Then simplify: \( 12+x−12=20-12 → x=8 \)

Solve Equations – Example 2:

Solve the equation.

\(3x=15\)

Solution:

\(3x=15\) is a linear equation having a single variable in it. Here, the operation is multiplication (variable \(x\) is multiplied by \(3\)) and its inverse operation is division. To solve this equation, divide both sides of the equation by \(3\):
\(3x=15→ 3x÷3=15÷ 3→x=5\)

Exercises for Solve Equations

Solve each equation.

1. \(\color{blue}{6x-30=6}\)
2. \(\color{blue}{7x=21 }\)
3. \(\color{blue}{22+x=45}\)
4. \(\color{blue}{8x+1=17}\)

1. \(\color{blue}{6}\)
2. \(\color{blue}{3}\)
3. \(\color{blue}{23}\)
4. \(\color{blue}{2}\)