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

7(-8x+7)=2(6x+4)

Solve the following equation for $x$ . Express your answer in the simplest form. $\newline$ $7(-8 x+7)=2(6 x+4)$ $\newline$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Solve the following equation for

x

. Express your answer in the simplest form.

\newline

7(-8 x+7)=2(6 x+4)

\newline

Distribute and Simplify: First, distribute the $7$ into the terms inside the parentheses on the left side of the equation and the $2$ into the terms inside the parentheses on the right side of the equation. $7(-8x + 7) = 2(6x + 4)$ $-56x + 49 = 12x + 8$
Move Terms: Next, move all the $x$ terms to one side of the equation and the constant terms to the other side by adding $56x$ to both sides and subtracting $8$ from both sides. $\newline$ $-56x + 56x + 49 = 12x + 56x + 8 - 8$ $\newline$ $49 = 68x$
Divide to Solve: Now, divide both sides of the equation by $68$ to solve for $x$ . $\newline$ $\frac{49}{68} = \frac{68x}{68}$ $\newline$ $x = \frac{49}{68}$
Simplify Fraction: Finally, simplify the fraction if possible. In this case, $49$ and $68$ do not have any common factors other than $1$ , so the fraction is already in its simplest form. $\newline$ $x = \frac{49}{68}$

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