Question

Simplify and solve the following linear equations.
 $3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17$
A. $z = 2$
B. $z = 9$
C. $z = 3$
D. $z = 7$

Answer 1

Hint: To solve these questions, always start by opening the parenthesis and multiplying the terms inside the parenthesis with the terms outside it. Then, collect all the variables present in the equation on one side of the equation and the constants on the other side. Then, simplify the equation obtained to get the final answer.

Complete step by step solution:
Given, $3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17$,
Now, start by multiplying the terms outside the parentheses to the terms inside them, on both the sides, to get,
$ \Rightarrow 3(5z) - 3(7) - 2(9z) + 2(11) = 4(8z) - 4(13) - 17$
Now, further, simplify the above equation,
$ \Rightarrow 15z - 21 - 18z + 22 = 32z - 52 - 17$
Taking all the variables on the left-hand side of the equation and the constants to the right-hand side of the equation, we get,
$ \Rightarrow 15z - 18z - 32z = - 52 - 17 + 21 - 22$
Now, simplify the above expression by further adding and subtracting the like terms, to get,
$ \Rightarrow - 35z = - 70$
Cancelling the negative signs from both the sides of the equation, we get,
$ \Rightarrow 35z = 70$
Now, divide both the sides of the equation by $\:35$ , to get,
$ \Rightarrow z = \dfrac{{70}}{{35}}$
On simplification of the above expression, we get,
$ \Rightarrow z = 2$
Hence, the value of the given linear equation after simplifying and solving it, is $z = 2$ .

Option A is the correct answer.

Additional Information: Linear equations can be expressed in one variable as well as in two variables. The general form of a linear equation in one variable can be given as $ax + b = 0$ , where $a \ne 0$ . The solution of such an equation can be given as $x = \dfrac{{ - b}}{a}$ .

Note: One must try to simplify the equation by shifting all the like terms to one side of the equation i.e. all the variables on one side of the equation and the constants on the other. One must remember the rules of multiplication of $+$ and $-$ while opening the parenthesis.