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Solving Equations: (lesson 1 of 4)

Solving Linear Equations

Equations with no parentheses

Example 1

Solve 5x - 4 - 2x + 3 = -7 - 3x + 5 + 2x

Solution 1

Step 1: Combine the similar terms

Linear Equation Solution
Linear Equation no parentheses

Step 2: Add x to both sides.

Linear Equation no parentheses
Linear Equation no parentheses

Step 3: Add 1 to both sides.

Linear Equation no parentheses
Linear Equation no parentheses

Step 4: Divide both sides by 4:

Linear Equation no parentheses
Solution is: Linear Equation no parentheses

Exercise 1: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4

Equations with parentheses

Example 2

Solve Linear Equation Example

Solution 2

Step 1: Simplify both sides:

Linear Equation parentheses
Linear Equation parentheses
Linear Equation parentheses

Step 2: Subtract x from both sides.

Linear Equation parentheses
Linear Equation parentheses

Step 3: Divide both sides by -3:

Linear Equation parentheses
Solution is: Linear Equation parentheses

Exercise 2: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4

Equations containing fractions

Example 3

Solve Linear Equation Example

Solution 3

Step 1: Multiply both sides by the LCD. Lowest common multiple of 2 and 3 is 6. So, we multiply both sides by 6.

Linear Equation with fractions

Step 2: Remove brackets:

Linear Equation with fractions

Step3: This problem is similar the previous

Linear Equation with fractions
Linear Equation with fractions
Linear Equation with fractions
Linear Equation with fractions
Linear Equation with fractions
Linear Equation with fractions

Solution is:

Linear Equation with fractions

Exercise 3: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4

More Complicated Example

Example 4

Linear Equation Example

Solution 4

In this case the LCD is (x + 2)(x - 10). Here is the complete solution to this problem.

Linear Equation Example

Much more Complicated Example

Example 5

Linear Equation Example

Solution 4

The first step is to factor the denominators

Linear Equation Example

The LCD is (x + 3)(x + 2). The solution is:

Linear Equation Example

Exercise 4: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4