# 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

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. $$\color{blue}{2}$$

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