Directions: Solve Each Of The Following Equations.1. $10t + 8t - 2t = 16$2. $24m + 24m = 96$3. $26 = 11n + 2n$4. $20a - 3a = 34$5. $180x + 4 = 64$6. $15x - 25 = 200$7. $5s + 3s = 32$8.
In this article, we will guide you through the process of solving a series of linear equations. These equations are in the form of ax + b = c, where a, b, and c are constants. We will use basic algebraic techniques to isolate the variable and find its value.
1.
To solve this equation, we need to combine like terms. The like terms in this equation are the terms with the variable t. We can combine the terms as follows:
10t + 8t - 2t = 16
First, we combine the terms with the variable t:
18t - 2t = 16
Next, we combine the like terms:
16t = 16
Now, we can isolate the variable t by dividing both sides of the equation by 16:
t = 16/16
t = 1
Therefore, the value of t is 1.
2.
To solve this equation, we need to combine like terms. The like terms in this equation are the terms with the variable m. We can combine the terms as follows:
24m + 24m = 96
First, we combine the terms with the variable m:
48m = 96
Now, we can isolate the variable m by dividing both sides of the equation by 48:
m = 96/48
m = 2
Therefore, the value of m is 2.
3.
To solve this equation, we need to combine like terms. The like terms in this equation are the terms with the variable n. We can combine the terms as follows:
26 = 11n + 2n
First, we combine the terms with the variable n:
26 = 13n
Now, we can isolate the variable n by dividing both sides of the equation by 13:
n = 26/13
n = 2
Therefore, the value of n is 2.
4.
To solve this equation, we need to combine like terms. The like terms in this equation are the terms with the variable a. We can combine the terms as follows:
20a - 3a = 34
First, we combine the terms with the variable a:
17a = 34
Now, we can isolate the variable a by dividing both sides of the equation by 17:
a = 34/17
a = 2
Therefore, the value of a is 2.
5.
To solve this equation, we need to isolate the variable x. We can do this by subtracting 4 from both sides of the equation:
180x + 4 - 4 = 64 - 4
180x = 60
Now, we can isolate the variable x by dividing both sides of the equation by 180:
x = 60/180
x = 1/3
Therefore, the value of x is 1/3.
6.
To solve this equation, we need to isolate the variable x. We can do this by adding 25 to both sides of the equation:
15x - 25 + 25 = 200 + 25
15x = 225
Now, we can isolate the variable x by dividing both sides of the equation by 15:
x = 225/15
x = 15
Therefore, the value of x is 15.
7.
To solve this equation, we need to combine like terms. The like terms in this equation are the terms with the variable s. We can combine the terms as follows:
5s + 3s = 32
First, we combine the terms with the variable s:
8s = 32
Now, we can isolate the variable s by dividing both sides of the equation by 8:
s = 32/8
s = 4
Therefore, the value of s is 4.
8.
To solve this equation, we need to combine like terms. The like terms in this equation are the terms with the variable y. We can combine the terms as follows:
7y - 2y = 18
First, we combine the terms with the variable y:
5y = 18
Now, we can isolate the variable y by dividing both sides of the equation by 5:
y = 18/5
y = 3.6
Therefore, the value of y is 3.6.
In this article, we will provide answers to frequently asked questions related to solving linear equations. These questions cover various topics, including combining like terms, isolating variables, and solving for unknown values.
Q: What are like terms in a linear equation?
A: Like terms in a linear equation are terms that have the same variable and coefficient. For example, in the equation 2x + 3x = 5, the terms 2x and 3x are like terms because they both have the variable x and the same coefficient (2 and 3, respectively).
Q: How do I combine like terms in a linear equation?
A: To combine like terms in a linear equation, you need to add or subtract the coefficients of the like terms. For example, in the equation 2x + 3x = 5, you can combine the like terms by adding the coefficients: 2x + 3x = 5x.
Q: How do I isolate a variable in a linear equation?
A: To isolate a variable in a linear equation, you need to get the variable by itself on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by a constant. For example, in the equation 2x + 3 = 5, you can isolate the variable x by subtracting 3 from both sides of the equation: 2x = 5 - 3, 2x = 2.
Q: What is the order of operations in solving a linear equation?
A: The order of operations in solving a linear equation is:
- Parentheses: Evaluate any expressions inside parentheses.
- Exponents: Evaluate any exponential expressions.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.
Q: How do I solve a linear equation with fractions?
A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, in the equation 1/2x + 1/4x = 3/4, you can eliminate the fractions by multiplying both sides of the equation by 4: 2x + x = 3.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable is 1. For example, the equation 2x + 3 = 5 is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation x^2 + 2x + 1 = 0 is a quadratic equation.
Q: How do I solve a system of linear equations?
A: To solve a system of linear equations, you need to find the values of the variables that satisfy all the equations in the system. You can do this by using various methods, such as substitution, elimination, or graphing.
Q: What is the importance of solving linear equations?
A: Solving linear equations is an essential skill in mathematics and other fields. It is used to model real-world problems, make predictions, and make decisions. Linear equations are used in a wide range of applications, including physics, engineering, economics, and computer science.
In conclusion, solving linear equations is a fundamental skill in mathematics and other fields. By understanding the concepts of like terms, isolating variables, and solving for unknown values, you can solve a wide range of linear equations and apply them to real-world problems.