Solve for x: 2(-5x - 1) + 4x - 3 = 19

Understand the Problem

The question is asking us to solve the equation for the variable x. This involves simplifying the left-hand side and isolating x to find its value.

Answer

$ x = -4 $

Steps to Solve

Distribute in the equation

First, distribute the $2$ into the parentheses: $$ 2(-5x - 1) = -10x - 2 $$ This changes the equation to: $$ -10x - 2 + 4x - 3 = 19 $$

Combine like terms

Now, combine the like terms on the left side of the equation: $$ -10x + 4x - 2 - 3 = -6x - 5 $$ So the equation now reads: $$ -6x - 5 = 19 $$

Isolate the variable

Next, add $5$ to both sides to isolate the term with $x$: $$ -6x - 5 + 5 = 19 + 5 $$ This simplifies to: $$ -6x = 24 $$

Solve for $x$

Finally, divide both sides by $-6$ to solve for $x$: $$ x = \frac{24}{-6} = -4 $$

The final answer is ( x = -4 ).

More Information

This solution involves distributing, combining like terms, and isolating the variable. It illustrates key algebraic manipulations used to solve linear equations.

Tips

Forgetting to distribute correctly.
Failing to combine like terms accurately.
Incorrectly isolating the variable by not accounting for signs.

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