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

2(-6x-7)=-3(4x+5)

Solve the following equation for $x$ . Express your answer in the simplest form. $\newline$ $2(-6 x-7)=-3(4 x+5)$ $\newline$

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Solve quadratic inequalities

Full solution

Q. Solve the following equation for

x

. Express your answer in the simplest form.

\newline

2(-6 x-7)=-3(4 x+5)

\newline

Distribute numbers: Distribute the numbers outside the parentheses to the terms inside the parentheses. $\newline$ $2 \times -6x = -12x$ $\newline$ $2 \times -7 = -14$ $\newline$ $-3 \times 4x = -12x$ $\newline$ $-3 \times 5 = -15$ $\newline$ So the equation becomes: $\newline$ $-12x - 14 = -12x - 15$
Simplify terms: Simplify both sides of the equation by combining like terms. $\newline$ On the left side, we have $-12x - 14$ , which is already simplified. $\newline$ On the right side, we have $-12x - 15$ , which is also already simplified. $\newline$ So the equation remains: $\newline$ $-12x - 14 = -12x - 15$
Isolate variable: Attempt to isolate $x$ on one side of the equation. $\newline$ We can try to add $12x$ to both sides to move the $x$ terms to one side: $\newline$ $-12x - 14 + 12x = -12x - 15 + 12x$ $\newline$ This simplifies to: $\newline$ $-14 = -15$
Recognize no solution: Recognize that the $x$ terms have cancelled out, leaving an equation that does not contain the variable $x$ . $\newline$ Since $-14 \neq -15$ , this indicates that there is no solution for $x$ that would satisfy the original equation.

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