Question

How do you solve the linear equation \[15\left( -42x+40 \right)=15\left( -8x+244 \right)\]?

Answer 1

Hint: In order to find the solution of the given question that is to find how to solve \[15\left( -42x+40 \right)=15\left( -8x+244 \right)\] and find the value of \[x\], apply one of the properties of addition, subtraction and division to simplify the expression and then take the terms with variable on one and other terms on the right side to get the value of variable \[x\].

Complete step by step solution:
According to the question, given equation in the question is as follows:
\[15\left( -42x+40 \right)=15\left( -8x+244 \right)\]
To solve the above equation, divide \[15\] to both the side of the equation, we will have:
\[\Rightarrow \dfrac{15\left( -42x+40 \right)}{15}=\dfrac{15\left( -8x+244 \right)}{15}\]
After simplifying the above equation, we will have:
\[\Rightarrow -42x+40=-8x+244\]
Now subtract the term \[40\] on both the sides, we will have:
\[\Rightarrow -42x+40-40=-8x+244-40\]
After simplifying the above equation with the help of subtraction, we will have:
\[\Rightarrow -42x=-8x+204\]
Now take all the like terms like one with variable \[x\] to left-hand side of the above equation and rest to the right-hand side, we will have:
\[\Rightarrow -42x+8x=204\]
After solving the terms in the left-hand side of the above equation with the help of addition, we will have:
\[\Rightarrow -34x=204\]
Now divide \[-34\] to both the sides of the above equation, we will have:
\[\Rightarrow \dfrac{-34x}{-34}=\dfrac{204}{-34}\]
After simplifying the above equation with the help of division, we will have:
\[\Rightarrow x=-6\]
Therefore, after solving the equation \[15\left( -42x+40 \right)=15\left( -8x+244 \right)\], the value of variable \[x\] is \[-6\].

Note: Students make mistakes in miscalculations while taking terms with variables on one side say left and other terms on the right side, it’s important to cross check the answer again once solved to avoid miscalculations while solving this type of questions.