n - 5 = 8
I assume that you are referring to:x = 5 + nIf n is a negative number, x is less than 5.ANSWER: x is less than 5 ...[ x < 5 ]
The number works out as 14
2n-4
8n - 9 = 17
The general idea is to solve one of the equations for one variable - in terms of the other variable or variables. Then you can substitute the entire expression into another equation or other equations; as a result, if it works you should end up having one less equation, with one less variable.
I assume that you are referring to:x = 5 + nIf n is a negative number, x is less than 5.ANSWER: x is less than 5 ...[ x < 5 ]
The number works out as 14
2n-4
8n - 9 = 17
You can write an equivalent equation from a selected equation in the system of equations to isolate a variable. You can then take that variable and substitute it into the other equations. Then you will have a system of equations with one less equation and one less variable and it will be simpler to solve.
8<(4n+10)
The general idea is to solve one of the equations for one variable - in terms of the other variable or variables. Then you can substitute the entire expression into another equation or other equations; as a result, if it works you should end up having one less equation, with one less variable.
If the number is n then twice the number is 2n and 7 less than twice the number is 2n - 7This could also be a boolean variable based on another variable. If the number is less than or equal to 3.5, the variable is false. Otherwise, it is true.
The relevant expression (not equation) is:2*(n + 8) - 4 or2n + 8 - 4
Let's represent the number as (x). The phrase "Eight less than five times a number" can be translated to (5x - 8), and "is seven more than the number" can be translated to (x + 7). Therefore, the algebraic equation representing the given phrase is (5x - 8 = x + 7).
That's exactly the purpose of the substitution method ... to get an equation with one less variable. When you have it, you solve it for the variable that's left.
To write out the given statement algebraically, you would start by defining the variable for the number, let's say it is represented by 'x'. The equation would be: 6x - 5 < 2x + 10. This equation represents the statement "Six times a number minus five is less than twice the number plus ten" in algebraic form. To solve this inequality, you would isolate the variable 'x' by performing operations to simplify and find the range of values that satisfy the inequality.