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Get ready to solve the puzzle: three numbers in a row that equal 114. We’ll show you a straightforward way to find those specific numbers.
The sum of three consecutive natural numbers is 114. Find the numbers.
Let’s denote the three consecutive natural numbers as x, x+1, and x+2.
The sum of these three numbers is given as 114:
x+(x+1)+(x+2)=114
Combine like terms:
3x+3=114
Subtract 3 from both sides:
3x=111
Divide by 3:
x=37
So, the three consecutive natural numbers are 37, 38, and 39.
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Linear Equations in Algebra
A linear equation is an equation in which the highest power of any variable is 1. In other words, there are no variables squared or cubed, and there are no variables multiplied together.
Here are some examples of linear equations:
- 3x + 2 = 5
- y – 4 = 7
- 2x – 3y = 10
Linear equations can be written in different forms, but the most common forms are:
- Slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
- Standard form: Ax + By = C, where A, B, and C are constants.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a point on the line and m is the slope of the line.
There are many ways to solve linear equations. Some common methods include:
- Graphing: Plot the equation on a coordinate plane and find the point where the line intersects the x-axis or the y-axis.
- Substitution: Solve for one variable in terms of the other and then substitute that value into the equation to solve for the other variable.
- Elimination: Add or subtract the equations together in a way that one of the variables cancels out, and then solve for the remaining variable.
Linear equations have many applications in real life. For example, they can be used to model the relationship between two variables, such as the price of a product and the quantity of the product that is sold. They can also be used to solve problems in physics, chemistry, economics, and many other fields.
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