Question

How do you solve \[10(2x+4)=-(-8-9x)+3x\]?

Answer 1

Hint: We will begin with opening up the brackets on each side of the equality. Then we will calculate separately each side of the equality. We then have to separate the \[x\] terms and the constants we get, after calculating the individual side. We further proceed with adding up similar terms and making the expression in terms of \[x\]. Hence, we get the value of \[x\].

Complete step by step solution:
According to the given question, we have an expression which we have to solve for \[x\].
We will start solving the expression by taking the LHS and RHS separately and solving it and then afterwards equating it back.
We have the expression as:
\[10(2x+4)=-(-8-9x)+3x\]-----(1)
Taking the LHS (left hand side) of the equality, we have,
\[10(2x+4)\]
Multiplying 10 to both the terms within the brackets, we get,
\[\Rightarrow 10(2x)+10(4)\]
Multiplying the terms, we have,
\[\Rightarrow 20x+40\]-----(2)
We have solved the LHS part, we will now be taking the RHS (right hand side) of the equality, we have,
\[-(-8-9x)+3x\]
 Opening the brackets, the negative sign outside the brackets will change the sign of the terms within the brackets, and so we have,
\[\Rightarrow 8+9x+3x\]
Adding up the similar terms, we get,
\[\Rightarrow 8+12x\]----(3)
Now, we will equate the equations (2) and (3), we get,
\[20x+40=8+12x\]----(4)
Now we will have to separate the \[x\] terms and the constants, we will use the properties of subtraction.
Subtracting 40 from both sides of equation (4),
\[\Rightarrow 20x+40-40=8+12x-40\]
Calculating the above expression, we get,
\[\Rightarrow 20x=12x-32\]
Now , we will subtract \[12x\] from both sides of the above expression, we get,
\[\Rightarrow 20x-12x=12x-32-12x\]
Solving it further in terms of \[x\], we have,
\[\Rightarrow 8x=-32\]
\[\Rightarrow x=-4\]

Therefore, the value of \[x=-4\].

Note: In the RHS of the given expression, we had a negative sign outside the bracket and so we need to make sure that the negative sign is not for the entire RHS, but is localised only for that bracket before which it is placed. Also, we need to make sure there is a reversal in the signs of the terms when the bracket is opened.
\[-(a+b)=-a-b\]