Question

How do you simplify and solve the equation 5m-3[7-(1-2m)]=0?

Answer 1

Hint: This type of problem is based on the concept of linear equations with one variable. First, we have to consider the whole linear equation with one variable. Take the negative sign inside the LHS and expand the equation. Then, add the constants and m terms. Use a distributive property which is \[a\left( b+c \right)=ab+ac\], in the obtained equation. Here, a=-3, b=6 and c=2m. Then, add 18 on both the sides of the equation. And divide the whole equation by -1 to get the value of m which is the required answer.

Complete step by step solution:
According to the question, we are asked to simplify and solve the equation
5m-3[7-(1-2m)]=0.
We have been given the equation is 5m-3[7-(1-2m)]=0. -----(1)
We first have to first simplify the given equation.
Let us remove the bracket of the LHS of the equation and multiply negative signs to each term inside the open bracket.
\[\Rightarrow 5m-3\left[ 7-1-\left( -2m \right) \right]=0.\]
We know that –(-x)=x. using this property in the above equation, we get
\[5m-3\left[ 7-1+2m \right]=0.\]
On further simplification, we get
\[5m-3\left[ 6+2m \right]=0\]
Let us simplify the equation further using distributive property, that is \[a\left( b+c \right)=ab+ac\].
Here, we find that a=-3, b=6 and c=2m.
Therefore, we get
\[\Rightarrow 5m-3\times 6-3\times 2m=0\]
We know that \[3\times 6=18\] and \[3\times 2=6\]. We get
\[5m-18-6m=0\]
Now, let us group the m terms and add them.
\[\Rightarrow \left( 5-6 \right)m-18=0\]
On further simplification, we get
\[-m-18=0\]
Let us take negative signs common from both the terms.
\[\Rightarrow -\left( m+18 \right)=0\]
Now, let us divide the whole equation by -1.
\[\Rightarrow \dfrac{-\left( m+18 \right)}{-1}=\dfrac{0}{-1}\]
We know that 0 divided by any term is zero.
\[\Rightarrow \dfrac{-\left( m+18 \right)}{-1}=0\]
On cancelling -1 from the numerator and denominator of the LHS, we get
\[m+18=0\]
Therefore, the simplified form of the equation is m+18=0
Now, we have to find the value of m.
We have to subtract 18 from both the sides of the equation. We get
\[m+18-18=0-18\]
\[\Rightarrow m+18-18=-18\]
We know that terms with the same magnitude and opposite signs cancel out. On cancelling 18, we get
\[m=-18\]
Therefore, the value of m is -18.

Hence, the simplified form of the equation 5m-3[7-(1-2m)]=0 is m+18=0 and the value of m is -18.

Note: We can check whether the answer obtained is correct or not.
Consider the LHS of the equation
LHS=5m-3[7-(1-2m)]
But, we know that x=-18. On substituting the value of x, we get
LHS=5(-18)-3[7-(1-2(-18))]
On further simplification, we get
LHS=5(-18)-3[7-(1-(-36))]
We know that –(-x)=x. using this property, we get
LHS=5(-18)-3[7-(1+36)]
LHS=5(-18)-3[7-37)]
On further simplification, we get
LHS=-90-3(-30)
LHS=-90+90
Therefore, LHS=0
Now, consider RHS.
RHS=0.
Here, LHS=RHS.
Therefore, the obtained answer is verified.