Question

How do you solve $2\left( {8x - 1} \right) + 7\left( {x + 5} \right) = - 59$?

Answer 1

Hint: In this question, we want to solve the linear equation of one variable. A linear equation of one variable can be written in the form $ax + b = c$. Here, a, b, and c are constants. And the exponent on the variable of the linear equation is always 1. To solve the linear equation, we have to remember that addition and subtraction are the inverse operations of each other. For example, if we have a number that is being added that we need to move to the other side of the equation, then we would subtract it from both sides of that equation.

Complete step-by-step answer:
In this question, we want to solve the linear equation of one variable.
The given equation is,
$ \Rightarrow 2\left( {8x - 1} \right) + 7\left( {x + 5} \right) = - 59$
Let us solve this equation, we first open the bracket.
$ \Rightarrow 16x - 2 + 7x + 35 = - 59$
Let us add the like terms.
$ \Rightarrow 23x + 33 = - 59$
Let us subtract 33 on both sides.
$ \Rightarrow 23x + 33 - 33 = - 59 - 33$
The subtraction of 33 and 33 is 0 on the left-hand side. And the subtraction of -59 and 33 is -92 on the right-hand side.
That is equal to,
$ \Rightarrow 23x = - 92$
Let us divide both sides by 23.
$ \Rightarrow \dfrac{{23x}}{{23}} = - \dfrac{{92}}{{23}}$
 The division of 23 and 23 is 0 on the left-hand side. And the division of 92 and 23 is 4 on the right-hand side.
That is equal to,
$ \Rightarrow x = - 4$
Hence, the solution of the given equation is -4.

Note:
Let us verify the answer.
$ \Rightarrow 2\left( {8x - 1} \right) + 7\left( {x + 5} \right) = - 59$
Let us substitute the value of x is equal to -4 in the above equation.
$ \Rightarrow 2\left( {8\left( { - 4} \right) - 1} \right) + 7\left( { - 4 + 5} \right) = - 59$
That is equal to,
$ \Rightarrow 2\left( { - 32 - 1} \right) + 7\left( { - 4 + 5} \right) = - 59$
$ \Rightarrow 2\left( { - 33} \right) + 7\left( 1 \right) = - 59$
$ \Rightarrow - 66 + 7 = - 59$
Let us apply addition on the left-hand side.
$ \Rightarrow - 59 = - 59$
Hence, the answer we get is correct.