Algebra Lesson 1.6: Testing a Possible Solution to an Equation

Practice Exercises:

Determine if the given value of \(x\) is a solution to the equation:

     1. \(4x+2=14\); \(x=3\)
     2. \(2(x+4)=x+6\); \(x=1\)
     3. \(\frac{1}{3}(x-6)+4 = \frac{3}{2}x + 2\); \(x=0\)
     4. \(x-2 = 11-8x\); \(x = -2\)

Solutions video:

Algebra Lesson 1.5: Solving Equations with Parentheses

Practice Exercises:

In the following exercises, use the distributive property to get rid of the parentheses. Then solve for \(x\).

     1. 4(x+3) = 20
     2. 0=3(x-7)
     3. 2(3x-3)=12

Solutions video:

Another Practice Problem:

In the following exercise, use the distributive property to get rid of the parentheses on both sides. Then solve for \(x\).

     4. 4(3x-3)+1=2-4(x+3)

Solution video:

Here are some more challenging problems involving fractions:

     5. \(\frac{1}{3}(5y-2)+2y=y-\frac{1}{3}(2+3y)\)
     6. \( -\frac{1}{7}(2z-2)=\frac{3}{7}(6-z)\)
     7. \( 5(\frac{1}{10}t-2)=3(t+1)-\frac{1}{2}t\)

Algebra Lesson 1.4: Solving Equations with x on Both Sides

Practice Exercises:

In the following exercises, use the three steps shown in the video above to solve for \(x\).

     1. \(2x-7 = 3-3x\)
     2. \(x= 5x+1\)
     3. \(\frac{1}{2}x + 2 = \frac{3}{2}x - 4\)
     4. \(x+2 = 11-8x\)

Solutions video:

Algebra Lesson 1.3: Combining Lessons 1.1 and 1.2 to Solve Two-Step Equations

Practice Exercises:

In the following exercises, use addition, subtraction, multiplication and division to solve for \(x\).

     1. \(6x+3 = 9\)
     2. \(15= 7x+1\)
     3. \(\frac{1}{3}x -\frac{5}{3} = 0\)
     4. \(11x - 9 = 24\)

Solutions video:

Algebra Lesson 1.2: Solving Equations by Multiplying and Dividing

Practice Exercises:

In the following exercises, use multiplication or division to solve for \(y\).

     1. \(3y = 6\)
     2. \(\frac{1}{2}y = 2\)
     3. \(0 = 4y\)

Solutions video:

Algebra Lesson 1.1: Solving Equations by Adding and Subtracting

Practice Exercises:

In the following exercises, use addition or subtraction to solve for \(x\).

     1. \(x-4 = 11\)
     2. \(x+3 = -2\)
     3. \(1+x = 7\)
     4. \(13=7+x\)
     5. \(2+x=0\)

Solutions video: