Question

How do you solve 4x+7 = 3x+18?

Answer 1

Hint: To solve the given linear equation, we need to reorder the terms (i.e.) move the ‘x’ terms to the left-hand side and constant terms to the right-hand side. After combining the like terms, calculate the ‘x’ terms and constant terms separately. After that we can get the ‘x’ value.

Complete step by step answer:
The given linear equation is 4x+7 = 3x+18. For solving the linear equation firstly, we have to combine the like terms. For that take 3x to the left-hand side then the sign of that term will change from positive to negative.
In the same way, if you take 7 to the right-hand side then again sign changes from positive to negative.
Reorder the terms, we get
4x-3x = 18-7
After re-ordering the equation subtract the coefficient of x in the left-hand side and constant term in the right-hand side. Coefficient of x is 4 ,3 and the constant terms are 18,7. Subtraction of 4x & 3x is 1x and 18 & 7 is 11.
 So, 4x-3x=1x and 18-7=11.
From the above calculation we get 1x = 11
Since 1x=x we can write x = 11
Therefore, the value of x from the given linear equation is 11.

Note:
Arrange the terms properly with the correct sign. Otherwise, you will get the wrong value of ‘x’.
When a term moves to the other side of the equation, its operation changes to the inverse operations. The inverse operation of an addition is a subtraction and multiplication is division.
Alternate method is time consuming because of double writing of the terms (variables, letters, numbers, constants) on both sides of the equation in every solving step. But the previous method follows the moving terms on both sides of the equation using a simple rule: “no new terms added, no missing terms after every move”.
Alternate Method:
The given equation is 4x+7 = 3x+18.
Step 1:
Subtract 7 from both sides of the equation.
4x+7 = 3x+18
4x+7-7 = 3x+18-7
Step 2:
Subtract the numbers.
4x = 3x+11
Step 3:
Subtract 3x from both sides of the equation.
4x-3x = 3x+11-3x
Step 4:
After simplification we get,
1x = 11
\[\Rightarrow x\text{ }=\text{ }11\]
Thus, the required value of x is 11.