Linear equations can be solved by applying various operations to both sides of the equal sign. These operations can help us simplify the equation, solve for the variable, and ultimately find the solution.

In this article, we will look at a brief summary of linear equations, followed by 20 examples with answers to master the process of solving first-degree equations.

## How to solve linear equations?

Recall that linear equations are equations in which all variables have a maximum power of 1. For example, the equations and are linear equations.

To solve linear equations, we have to apply different operations to both sides of the equal sign, so that we can solve for the variable. Therefore, we can follow the following steps to find the solution to linear equations:

**Step 1:** We simplify the expression. This includes removing parentheses and other grouping signs, removing fractions, and combining like terms.

** Step 2:** We isolate the variable. We perform addition and subtraction to place all terms with variables on only one side of the equation.

** Step 3:** We solve the equation. We do multiplication and division to find the answer.

## 20 Linear equation examples with answers

The following 20 linear equation examples have their respective solution, where the process is indicated step by step. It is recommended that you try to solve the examples yourself before looking at the answer.

**EXAMPLE 1**

Solve the equation .

##### Solution

**Step 1:** Simplify: We have nothing to simplify here.

**Step 2:** Solve for the variable: We use addition to solve for the variable:

**Step 3:** Solve: We divide both sides by 5:

**EXAMPLE ****2**

Solve the equation .

##### Solution

**Step 1:** Simplify: We have nothing to simplify.

**Step 2:** Solve for the variable: We use addition and subtraction to solve for the variable:

**Step 3:** Solve: We divide both sides by 2:

**EXAMPLE ****3**

Find the value of *t* in the equation .

##### Solution

**Step 1:** Simplify: We do not have like terms.

**Step 2:** Solve for the variable: We use subtraction to solve for the variable:

**Step 3:** Solve: We divide both sides by 2:

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**EXAMPLE ****4**

Solve the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses:

**Step 2:** Solve for the variable: We use subtraction to solve for the variable:

**Step 3:** Solve: We divide both sides by 6:

**EXAMPLE ****5**

Solve the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses on both sides of the equation and combine like terms:

**Step 2:** Solve for the variable: We use addition and subtraction to solve for the variable:

**Step 3:** Solve: In this case, we no longer have to divide:

**EXAMPLE ****6**

Find the value of *z* in the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses and combine like terms:

**Step 2:** Solve for the variable: We use subtraction to solve for the variable:

**Step 3:** Solve: We divide both sides by -1:

**EXAMPLE ****7**

Solve the equation .

##### Solution

**Step 1:** Simplify: We multiply by 3 to eliminate the fraction:

**Step 2:** Solve for the variable: We subtract 1 and 3x from both sides:

**Step 3:** Solve: We divide both sides by -1:

**EXAMPLE ****8**

Solve the equation .

##### Solution

**Step 1:** Simplify: We multiply both sides of the equation by 3 to eliminate the fractions and combine like terms:

.

**Step 2:** Solve for the variable: We add 6 and subtract 2x from both sides:

**Step 3:** Solve: We divide both sides by 2:

**EXAMPLE ****9**

Find the value of t in the equation .

##### Solution

**Step 1:** Simplify: We multiply by 15 to eliminate the fractions and combine like terms:

.

**Step 2:** Solve for the variable: We subtract 15 and 5 *t* from both sides:

**Step 3:** Solve: We no longer have to divide:

**EXAMPLE ****10**

Solve the equation .

##### Solution

**Step 1:** Simplify: We multiply both sides by (*x*+1) and combine like terms:

**Step 2:** Solve for the variable: Add 1 and subtract 3 *x* from both sides:

**Step 3:** Solve: We no longer have to divide:

**EXAMPLE ****11**

Find the value of *t* in the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses and combine like terms:

**Step 2:** Solve for the variable: We add 40 and subtract *t* from both sides:

**Step 3:** Solve: We divide both sides by 6:

**EXAMPLE ****12**

Solve the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses and combine like terms:

**Step 2:** Solve for the variable: We subtract 6 and 3 *x* from both sides:

**Step 3:** Solve: We divide both sides by 6:

**EXAMPLE ****13**

Find the value of *x* in the equation .

##### Solution

**Step 1:** Simplify: We multiply the entire equation by 4 (*x*+2) and combine like terms:

**Step 2:** Solve for the variable: We subtract 20 and 9 *x* from both sides:

**Step 3:** Solve: We divide both sides by -1:

**EXAMPLE ****14**

Find the value of *y* in the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses and combine like terms:

**Step 2:** Solve for the variable: We add 11 and subtract 7*y* from both sides:

**Step 3:** Solve: We no longer have to divide:

**EXAMPLE ****15**

Solve the equation .

##### Solution

**Step 1:** Simplify: We multiply the entire equation by 3, expand the parentheses, and combine like terms:

**Step 2:** Solve for the variable: We add 3 and subtract 9 *x* from both sides:

**Step 3:** Solve: We divide both sides by -5:

**EXAMPLE ****16**

Find the value of *x* in the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses and combine like terms:

**Step 2:** Solve for the variable: We subtract 18 and subtract *x* from both sides:

**Step 3:** Solve: We divide both sides by -4:

**EXAMPLE ****17**

Find the value of *w* in the equation .

##### Solution

**Step 1:** Simplify: We expand the parentheses and combine like terms:

**Step 2:** Solve for the variable: We add 50 and subtract 4 *w* from both sides:

**Step 3:** Solve: We divide both sides by 16 and simplify the fraction:

**EXAMPLE ****18**

Find the value of *r* in the equation .

##### Solution

**Step 1:** Simplify: We multiply both sides by 2 to eliminate the fraction, expand the parentheses, and combine like terms:

**Step 2:** Solve for the variable: We add 22 and subtract *r* from both sides:

**Step 3:** Solve: We divide both sides by -13:

**EXAMPLE ****19**

Find the value of *x* in the equation .

##### Solution

**Step 1:** Simplify: We expand all the parentheses and combine like terms:

**Step 2:** Solve for the variable: We subtract 4 and 7 *x* from both sides:

**Step 3:** Solve: We divide both sides by -12:

**EXAMPLE ****20**

Find the value of *x* in the equation .

##### Solution

**Step 1:** Simplify: We start by simplifying the fraction, then multiply by 4 to eliminate the fractions and combine like terms:

**Step 2:** Solve for the variable: We subtract 12 and 3 *x* from both sides:

**Step 3:** Solve: We divide both sides by -1:

## See also

Interested in learning more about solving equations? Take a look at these pages:

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