Solve for $x$ and write your answer in simplest form. $\newline$ $-\frac{5}{4}-\left(\frac{3}{4} x+5\right)+7 x=-10 x$ $\newline$ Answer: $x=$

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Algebra 1

Evaluate piecewise-defined functions

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Q. Solve for

x

and write your answer in simplest form.

\newline

-\frac{5}{4}-\left(\frac{3}{4} x+5\right)+7 x=-10 x

\newline

Answer:

x=

Write Equation: First, let's write down the equation and simplify it by distributing the negative sign and combining like terms. $\newline$ The equation is: $\newline$ $-(5)/(4)-((3)/(4)x+5)+7x=-10x$
Distribute Negative Sign: Distribute the negative sign through the parentheses: $\newline$ $-(5)/(4) - (3)/(4)x - 5 + 7x = -10x$
Combine Like Terms: Combine like terms by adding $-(5)/(4)$ and $-5$ , and also by combining $7x$ and $-\frac{3}{4}x$ : $\newline$ $-\frac{5}{4} - 5 = -\frac{5}{4} - \frac{20}{4} = -\frac{25}{4}$ $\newline$ $7x - \frac{3}{4}x = \frac{28}{4}x - \frac{3}{4}x = \frac{25}{4}x$ $\newline$ Now the equation looks like this: $\newline$ $-\frac{25}{4} + \frac{25}{4}x = -10x$
Get X Terms Together: Next, we want to get all the x terms on one side and the constants on the other. To do this, we add $10x$ to both sides of the equation: $\newline$ $-\frac{25}{4} + \frac{25}{4}x + 10x = -10x + 10x$
Isolate X Term: Simplify the equation by combining like terms: $\newline$ $-\frac{25}{4} + \frac{25}{4}x + \frac{40}{4}x = 0$ $\newline$ $-\frac{25}{4} + \frac{65}{4}x = 0$
Solve for X: Now, isolate the x term by adding $\frac{25}{4}$ to both sides: $\newline$ $-\frac{25}{4} + \frac{25}{4} + \frac{65}{4}x = \frac{25}{4}$ $\newline$ $\frac{65}{4}x = \frac{25}{4}$
Simplify Fraction: Finally, solve for x by dividing both sides by $\frac{65}{4}$ : $\newline$ $x = \frac{25}{4} \div \frac{65}{4}$ $\newline$ $x = \frac{25}{4} \times \frac{4}{65}$ $\newline$ $x = \frac{25 \times 4}{4 \times 65}$ $\newline$ $x = \frac{25}{65}$
Simplify Fraction: Finally, solve for x by dividing both sides by $\frac{65}{4}$ : $\newline$ $x = \frac{25}{4} \div \frac{65}{4}$ $\newline$ $x = \frac{25}{4} \times \frac{4}{65}$ $\newline$ $x = \frac{25 \times 4}{4 \times 65}$ $\newline$ $x = \frac{25}{65}$ Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $5$ : $\newline$ $x = \frac{25 \div 5}{65 \div 5}$ $\newline$ $x = \frac{5}{13}$