Question
Question: How do you solve \(4x + 8 = 7x - 7\) ?...
How do you solve 4x+8=7x−7 ?
Solution
One must remember in algebra, only the terms having the same degree or power of the variable can be added or subtracted. Here, we shift all the terms with the same power on the same side of the equation and then performing the necessary operations, the value of x can be found.
Complete step-by-step answer:
As we know in algebra, only the terms having the same power on the variable can be added or subtracted.
Here, the terms 4x and 7x have the same power of x , and hence they can be added or subtracted from each other.
Similarly, the terms 8 and −7 have the same power of x , which is 0 because any number with a power of 0 is equal to 1 .
Hence, these terms can also be written as 8x0 and −7x0 . As they have the same power, these terms can be added or subtracted from each other.
To simplify the equation, let’s start by shifting the same power terms on the same side of the equation
The equation we are given here is
⇒ 4x+8=7x−7
Now, adding 7 on both the sides of the equation
⇒4x+8+7=7x−7+7
⇒4x+15=7x+0
Now, subtracting 4x from both sides of the equation
⇒4x+15−4x=7x−4x
Rearranging the terms,
⇒4x−4x+15=7x−4x
⇒0+15=7x−4x
Now, to explain the subtraction, let’s expand the terms 7x and 4x .
We know that 7x means 7 times x . Hence, expanding 7x as shown
⇒7x=x+x+x+x+x+x+x
Similarly, for 4x we can write
⇒4x=x+x+x+x
Substituting these expansions in the equation,
⇒15=(x+x+x+x+x+x+x)−(x+x+x+x)
Opening the brackets,
⇒15=x+x+x+x+x+x+x−x−x−x−x
⇒15=x+x+x
Here we have 3 times x which can be written as 3x ,
⇒15=3x
Dividing both the sides by 3 ,
⇒315=x
Factoring the numerator,
⇒35×3=x
**⇒x=5
This is the solution for the given equation. **
Note:
Another method for subtracting the terms with x is by taking the common factor i.e. variable x common and subtracting the numbers in the bracket. If one wants to check the accuracy of the solution, one can substitute the obtained value in the given equation and check if it satisfies the equation.