First-degree equations can be solved by applying different operations to both sides of the equal sign so that we simplify the equation and solve for the variable. In this article, we will look at a summary of solving first-degree equations. In addition, we will see several examples with answers and practice problems in order to improve the retention of mathematical concepts and processes.

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exercises of first degree equations

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Exploring first-degree equations with examples.

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linear equations with one variable

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Exploring first-degree equations with examples.

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Summary of first degree equations

Recall that first-degree equations are equations in which all variables have a maximum exponent of 1. For example, the equations 3x+2=6 and 4x+3=2x-1 are first degree equations.

To solve first-degree equations, we remember that we can apply any operation to the equation as long as we perform that operation on both sides of the equal sign. We can follow the following steps to solve first degree equations:

Step 1: Eliminate grouping signs and combine like terms.

Step 2: Solve for the terms with variables on one side of the equation.

Step 3: Use multiplication and division to isolate the variable completely and to find its value.


First degree equations – Examples with answers

The following first-degree equation examples can be used to fully understand the process of solving these equations. These solved examples show the procedure to follow step by step.

EXAMPLE 1

Solve the equation 4x+2=10.

Step 1: Simplify: We do not have grouping signs or like terms.

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

4x+2=10

4x+2-2=10-2

4x=8

Step 3: Solve: We use division to solve:

4x=8

\frac{4}{4}x=\frac{8}{4}

x=2

EXAMPLE 2

Find the value of x in the equation 5x-6=15-2x.

Step 1: Simplify: We do not have grouping signs or like terms.

Step 2: Solve for the variable: We use sums to solve for the variable:

5x-6=15-2x

5x-6+6=15-2x+6

5x=21-2x

5x+2x=21-2x+2x

7x=21

Step 3: Solve: We divide by 7 to solve:

7x=21

\frac{7}{7}x=\frac{21}{7}

x=3

EXAMPLE 3

Find the value of x in the equation 4(2x+4)=-8.

Step 1: Simplify: We expand the parentheses:

4(2x+4)=-8

8x+16=-8

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

8x+16=-8

8x+16-16=-8-16

8x=-24

Step 3: Solve: We divide by 8 to solve:

8x=-24

\frac{8}{8}x=\frac{-24}{8}

x=-3

EXAMPLE 4

Solve the equation 2(4x-11)=3(2x-4).

Step 1: Simplify: We expand the parentheses on both sides:

2(4x-11)=3(2x-4)

8x-22=6x-12

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

8x-22+22=6x-12+22

8x=6x+10

8x-6x=6x+10-6x

2x=10

Step 3: Solve: We divide by 2 to solve:

2x=10

\frac{2}{2}x=\frac{10}{2}

x=5

EXAMPLE 5

Solve the equation 5(x-2)-3=4(2x+3)-4x.

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

5(x-2)-3=4(2x+3)-4x

5x-10-3=8x+12-4x

5x-13=4x+12

Step 2: Solve for the variable: We solve using addition and subtraction:

5x-13+13=4x+12+13

5x=4x+25

5x-4x=4x+25-4x

x=25

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

x=25

EXAMPLE 6

Solve the equation \frac{5-2x}{3}=\frac{-x+7}{6}.

Step 1: Simplify: We multiply the entire equation by 6 to eliminate the fractions:

\frac{5-2x}{3}=\frac{-x+7}{6}

2(5-2x)=-x+7

10-4x=-x+7

Step 2: Solve for the variable: We solve using addition and subtraction:

10-4x-10=-x+7-10

-4x=-x-3

-4x+x=-x-3+x

-3x=-3

Step 3: Solve: We divide by -3 to solve:

\frac{-3}{-3}x={-3}{-3}

x=1

EXAMPLE 7

Solve the equation 4(2x-5)=\frac{x-1}{2}+3.

Step 1: Simplify: We multiply the entire equation by 2 to eliminate the fractions. Then we remove the parentheses and combine like terms:

4(2x-5)=\frac{x-1}{2}+3

8(2x-5)=x-1+6

16x-40=x+5

Step 2: Solve for the variable: We solve using addition and subtraction:

16x-40+40=x+5+40

16x=x+45

16x-x=x+45-x

15x=45

Step 3: Solve: We divide by 15 to solve:

\frac{15}{15}x=\frac{45}{15}

x=3


First degree equations – Practice problems

The following practice problems can be solved to test your knowledge about solving first-degree equations. Just choose an answer and click on “Check”. If you have trouble solving these problems, you can look at the solved examples above carefully.

Solve the equation 4x-2=2x+4.

Choose an answer






Solve the equation 4(x-2)=3x-10.

Choose an answer






Find the value of x in the equation 3x-3=3(2x-2)-15.

Choose an answer






Solve the equation \frac{3x-2}{2}=2x-3.

Choose an answer






Find the value of t en la equation \frac{x+3}{2}=\frac{x+6}{4}+\frac{1}{2}.

Choose an answer







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