Question
Question: How do you solve \(9w - 4(w - 2) = 3(w + 1) - 9\)?...
How do you solve 9w−4(w−2)=3(w+1)−9?
Solution
The given equation is a linear equation in one variable w. To solve the above equation, we need to find the value of w. We have to apply the Distributive property of multiplication in the given equation to solve and simplify.
Formula used: a(b+c)=ab+ac
Complete step by step solution:
We have to solve 9w−4(w−2)=3(w+1)−9 for the value of w.
Distributive property of multiplication states that,
a(b+c)=ab+ac
In the given equation 9w−4(w−2)=3(w+1)−9 we apply distributive property of multiplication to the expression 4(w−2) in the Left Hand Side or LHS and the expression 3(w+1) in the Right Hand Side or RHS.
⇒4(w−2)=4w−8and 3(w+1)=3w+3
Thus, we get:
9w−(4w−4×2)=(3w+3×1)−9 ⇒9w−(4w−8)=(3w+3)−9
Now we can simplify the above equation to shift all the terms with the variable w in the LHS and all other terms in the RHS.
⇒9w−4w−(−8)=3w+3−9 ⇒9w−4w+8=3w+3−9
Taking 3w from the RHS to the LHS and 8 from the LHS to the RHS, we get:
⇒9w−4w−3w=3−9−8 ⇒2w=−14
Thus, we see that
2w=−14 ⇒w=2−14=−7
Hence, the solution of the given equation is w=−7.
Additional Information: Distributive property of multiplication means to multiply the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Note: We can check whether our solution is correct or not by putting the resulting value of w in the original equation and comparing LHS with RHS. Putting w=−7 in LHS we get,
9w−4(w−2) =9×(−7)−4((−7)−2) =−63−4(−9) =−63+36 =−27
Putting w=−7 in RHS we get,
3(w+1)−9 =3(−7+1)−9 =3(−6)−9 =−18−9 =−27
Here, LHS=RHS=−27. Since LHS = RHS, we can say that our solution of w=−7 satisfies the equation and thus, the correct answer.