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Solve the following equation for
x. Express your answer in the simplest form.

-2(10 x-7)-7=-3(7x-1)-8

Solve the following equation for $x$ . Express your answer in the simplest form. $\newline$ $-2(10 x-7)-7=-3(7 x-1)-8$ $\newline$

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Write an equation word problem

Full solution

Q. Solve the following equation for

x

. Express your answer in the simplest form.

\newline

-2(10 x-7)-7=-3(7 x-1)-8

\newline

Distribute and Simplify: First, let's distribute the $-2$ across the $(10x - 7)$ and the $-3$ across the $(7x - 1)$ . $-2 \times 10x$ gives us $-20x$ , and $-2 \times -7$ gives us $+14$ . $-3 \times 7x$ gives us $-21x$ , and $(10x - 7)$ $0$ gives us $(10x - 7)$ $1$ .So the equation becomes $(10x - 7)$ $2$ .
Combine Like Terms: Now, let's simplify both sides of the equation by combining like terms. $\newline$ On the left side, $14 - 7$ simplifies to $7$ . $\newline$ On the right side, $3 - 8$ simplifies to $-5$ . $\newline$ The equation now is $-20x + 7 = -21x - 5$ .
Add and Subtract $x$ : Next, we'll add $21x$ to both sides to get all the $x$ terms on one side. $-20x + 21x + 7 = -21x + 21x - 5$ simplifies to $x + 7 = -5$ .
Solve for x: Then, we subtract $7$ from both sides to solve for $x$ . $\newline$ $x + 7 - 7 = -5 - 7$ simplifies to $x = -12$ .

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