4 ADDED TO 5 TIMES A NUMBER EQALS 2 SUBTRACTED FROM 7 TIMES THE NUMBER.FIND THE NUMBER
4 + 5n = 7n - 2
6 = 2n
Yes, n = 3
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To find the number, let's break down the given information and set up an equation.
First, we are told that "4 is added to 5 times a number." Let's represent the number as 'x'. So, the expression "5 times a number" would be 5x, and adding 4 to it gives us 5x + 4.
Next, we are told that this expression (5x + 4) is equal to "2 subtracted from 7 times the number." Similarly, "7 times the number" is 7x, and subtracting 2 from it gives us 7x - 2.
Now, we can set up the equation:
5x + 4 = 7x - 2
To solve this equation, we need to isolate the variable 'x'. Let's do that step by step:
First, we can simplify the equation by combining like terms on both sides:
5x - 7x = -2 - 4
-2x = -6
Next, we need to isolate 'x' by getting rid of the coefficient (-2) attached to it. To do that, we divide both sides of the equation by -2:
(-2x)/(-2) = (-6)/(-2)
x = 3
Therefore, the number is 3.
To double-check our solution, let's substitute x = 3 back into the original equation:
5(3) + 4 = 7(3) - 2
15 + 4 = 21 - 2
19 = 19
As both sides of the equation are equal, we can confirm that the solution x = 3 is correct.