Question

How do you solve 5x+4x+7 = x+15?

Answer 1

Hint: We are asked to find the solution of 5x+4x+7 = x+15. To solve for x, we will first learn about the linear equation in one variable, then we look to find the solution of 5x+4x+7 = x+15. We first try with the method of hit and trial in which we try to put the value of x which may be the solution, then we use another method in which we use the algebraic operation to simplify and solve the given problem.

Complete step by step answer:
We are given the expression 5x+4x+7 = x+15. We are asked to find the value of x, or we can say that we are asked to solve this expression.
We learn about equations in one variable, equation in one simple represents the equation that has one variable (say x, y or z) and others are constant. For example,
x+2 = y, 2-x = 2, 2x, 2y etc.
Our equation 5x+4x+7 = x+15 also has just one variable x.
We have to find the value of x which will satisfy our given equation.
Firstly, we will try the hit and trial method, where we will put the value of x and check if it satisfies our equation or not.
Let x = 0. Putting x = 0 in 5x+4x+7 = x+15. So, we get,
0 + 0 +7 = 0 + 15
So, we will get, 7 = 15 which is not true. Hence, x = 0 is not the solution.
Let x = -1. Putting x = -1 in 5x+4x+7 = x+15. So, we get,
5x (-1) + 4 (-1) + 7 = -1 + 15
-5-4+7 = -1+15
-2 = -14 which is not true. Hence, x = -1 is not the solution.
Let x = 2. Putting x = 2 in 5x+4x+7 = x+15. So, we get,
5x (2) + 4 (2) + 7 = 2 + 15
10+4+7 = 2+15
21 = 17, which is not true. Hence, x = 2 is not the solution.
Let x = 1. Putting x = 1 in 5x+4x+7 = x+15. So, we get,
5x (1) + 4 (1) + 7 = 1 + 15
5+4+7 = 1+15
16 = 16, which is true. Hence we get that x = 1 is the solution of our expression.
This method is very tricky and time-consuming and we may get a solution after many attempts.
We have another method in which we use the algebraic operation. We have, 5x+4x+7 = x+15.
We simplify the terms by adding like terms on both sides. So, we can write,
5x+4x = 9x. So, our expression, 5x+4x+7 = x+15 becomes 9x+7 = x+15.
Take terms containing x on the left side and the constants on the other side. So, we get,
9x-x = 15-7
On simplifying, we get,
8x = 3
On dividing both the sides by 8, we get,
x = 1
So, x = 1 is the solution of the expression 5x+4x+7 = x+15.

Note:
While solving this question, using the hit and trial method will be lengthy, as sometimes we may start from a point and move along say positive direction but our solution may lie in the negative direction, so we will keep finding and still might not get the solution. Hence, it is better to use the algebraic method where we cancel all the terms by addition, subtraction, multiplication, and division, this will make the solution short and we will be able to reach the solution easily.