Question

Simplify and solve the following linear equation:
 $ 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17 $

Answer 1

Hint: The best way to solve a linear equation in one variable is to rearrange the linear equation in such a way that we could write all the variable terms to the left hand side of the equation. And all the constant terms to the right hand side of the equation.

Complete step-by-step answer:
Linear equation is the equation with degree one. It does not have anything to do with the number of variables in the equation. A linear equation can have two, three or more variables in it as long as the degree of the equation is equal to one.
Linear equations graphically always represent a straight line. Linear equations in one variable give a line parallel to coordinate axes.
The given linear equation is,
 $ 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17 $
By opening the brackets to simplify, we can write
 $ 15z - 21 - 18z + 22 = 32z - 52z - 17 $
Simplify both the sides of the equation, we can write
 $ - 3z + 1 = - 20z - 17 $
Now, take the variable term to the left hand side of the equation and the constant term to the right hand side of the equation.
 $ \Rightarrow 20z - 3z = - 17 - 1 $
By simplifying it, we get
 $ 17z = - 18 $
 $ \Rightarrow z = - \dfrac{{18}}{{17}} $

Note: Be careful while opening the brackets. Especially the ones with the negative terms. Sign multiplication may lead to a mistake. So make sure the calculation done is correct. Remember that the sign of the term changes when you move it from one side to another side of the “equal to” sign. So don’t forget to change the sign of such terms.