2-4 skills practice solving equations with the variable on each side
2-4 Skills Practice Solving Equations with the Variable on Each Side
Solving equations with the variable on each side is an essential skill in algebra. This concept helps us find the value of a variable in an equation by isolating it on both sides of the equation. In this article, we will focus on 2-4 skills practice solving equations with the variable on each side.
Before we dive into the practice problems, lets quickly review the steps involved in solving equations with the variable on each side.
1. Simplify both sides of the equation if necessary by combining like terms and applying any applicable properties of equality.
2. Move all terms containing the variable to one side of the equation by adding or subtracting.
3. Simplify the resulting equation by combining like terms again.
4. Finally, divide both sides of the equation by the coefficient of the variable to solve for the variable.
Now that we have refreshed our memory on the steps, lets jump into some practice problems.
Problem 1:
Solve the equation 3x + 5 = 2x - 4.
Solution:
To solve this equation, we need to move all terms containing the variable to one side. To do this, we subtract 2x from both sides:
3x + 5 - 2x = 2x - 4 - 2x
x + 5 = -4
Next, we simplify the equation by combining like terms:
x + 5 - 5 = -4 - 5
x = -9
So the solution to the equation is x = -9.
Problem 2:
Solve the equation 6y + 4 = 2y - 1.
Solution:
To solve this equation, we need to move all terms containing the variable to one side. To do this, we subtract 2y from both sides:
6y + 4 - 2y = 2y - 1 - 2y
4y + 4 = -1
Next, we simplify the equation by combining like terms:
4y + 4 - 4 = -1 - 4
4y = -5
Finally, we divide both sides of the equation by the coefficient of the variable:
4y/4 = -5/4
y = -5/4
So the solution to the equation is y = -5/4.
Problem 3:
Solve the equation 2(x + 3) = 3x - 4.
Solution:
To solve this equation, we need to distribute the 2 to both terms inside the parentheses:
2x + 6 = 3x - 4
Next, we move all terms containing the variable to one side. To do this, we subtract 2x from both sides:
2x + 6 - 2x = 3x - 4 - 2x
6 = x - 4
Next, we move all terms without the variable to the other side:
6 + 4 = x - 4 + 4
10 = x
So the solution to the equation is x = 10.
Problem 4:
Solve the equation 5(2y - 3) = 3(4y + 1).
Solution:
To solve this equation, we need to distribute the 5 and 3 to both terms inside the parentheses:
10y - 15 = 12y + 3
Next, we move all terms containing the variable to one side. To do this, we subtract 12y from both sides:
10y - 15 - 12y = 12y + 3 - 12y
-2y - 15 = 3
Next, we move all terms without the variable to the other side:
-2y - 15 + 15 = 3 + 15
-2y = 18
Finally, we divide both sides of the equation by the coefficient of the variable:
-2y/-2 = 18/-2
y = -9
So the solution to the equation is y = -9.
By practicing these types of problems, you will become more comfortable with solving equations that have variables on each side. Remember to follow the steps we discussed earlier, and always simplify the equation as much as possible before solving for the variable. With enough practice, you will master this skill and be able to tackle more complex algebraic equations with confidence.
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