Solve for x and write your answer in simplest form. -(5)/(4)-((3)/(4)x+5)+7x=-10 x Answer: x=

Question

Solve for  x and write your answer in simplest form.  -(5)/(4)-((3)/(4)x+5)+7x=-10 x Answer:  x=

Bytelearn · Accepted Answer

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

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: $x=$

Full solution

More problems from Evaluate piecewise-defined functions

Related topics

Solve for x x x and write your answer in simplest form.\newline−54−(34x+5)+7x=−10x -\frac{5}{4}-\left(\frac{3}{4} x+5\right)+7 x=-10 x −45​−(43​x+5)+7x=−10x\newlineAnswer: x= x= x=

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: $x=$