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# Find the value of x for given equation: $3(5x + 7) + 5(2x - 11) = 3(8x - 5) - 15$

Last updated date: 20th Jun 2024
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Hint: This is a linear equation with one variable and constant terms. To solve such a type of linear equation, always arrange all variable terms on one side of the equation and all constant terms on the other side of the equation. So it will become the simple level linear equation. So here we will simplify the given terms and after that will arrange the terms and will find out the value of x.

Complete step-by-step solution:
Here the given equation is $3(5x + 7) + 5(2x - 11) = 3(8x - 5) - 15$. It is a linear equation with one variable and constant terms. Such type of linear equation can be easily solved by simplifying the given equation, arranging the terms of the equation. Arrange all variable terms on the one side of the equation and all constant terms on the other side of the equation.
So, here given equation is $3(5x + 7) + 5(2x - 11) = 3(8x - 5) - 15$
Using multiplication of the polynomial with the given constant terms to simplify the equation. In this multiplication constant term will be multiplied to all nominal of the polynomial with its sign.
So, $3(5x + 7) + 5(2x - 11) = 3(8x - 5) - 15$
So, $3 \cdot 5x + 3 \cdot 7 + 5 \cdot 2x - 5 \cdot 11 = 3 \cdot 8x - 3 \cdot 5 - 15$
Simplifying the terms, $15x + 21 + 10x - 55 = 24x - 15 - 15$
Arranging all terms of x on the left side of the equation and all constant terms on the right side of the equation,
So, $15x + 10x - 24x = - 15 - 15 - 21 + 55$
Taking out x common on left side of the equation, $(15 + 10 - 24)x = - 15 - 15 - 21 + 55$
Simplifying, $(1)x = 4$
So, $x = 4$

So, the value of x is 4.

Note: There is an alternative method to solve such a linear equation. In this method we have to make only the “x” term on the left side of the equation and the constant term on the right side of the equation. For this we have to add/subtract/multiply/divide the terms accordingly.
So, here $3(5x + 7) + 5(2x - 11) = 3(8x - 5) - 15$
Writing the simplified form as solved in above steps, $15x + 21 + 10x - 55 = 24x - 15 - 15$
Firstly add all terms on left and right side of the equation
So, $25x - 34 = 24x - 30$
Now add 34 in both side of the equation
So, $25x - 34 + 34 = 24x - 30 + 34$
As plus 30 and minus 34 will cancel out so, $25x = 24x + 4$
Now subtract 24x from both side of the equation,
So, $25x - 24x = 24x + 4 - 24x$
So, $x = 4$.
So the value of x is 4.