Accelerated Algebra 2 - CH. 1 Mixed Practice

Linear Equation: $-2(3x-7)+4(x-8)=22$

Solution: $x = -20$ (simplified steps: $-2x-18=22 \implies -2x=40$)

Fractional Linear Equation: $\frac{2}{3}\left(\frac{1}{3}x-9\right)=\frac{4}{9}-\frac{5}{9}x$

Solution: $x = \frac{93}{11}$ (cleared fractions to get $6x-81=12-5x \implies 11x=93$)

Garden Perimeter Word Problem

A garden has a perimeter of $220\,\text{ft}$ with length $8\,\text{ft}$ less than $3$ times the width. Solution: Width = $29.5\,\text{ft}$, Length = $80.5\,\text{ft}$ ($8x-16=220 \implies x=29.5$)

Three Numbers Sum Word Problem

The sum of three numbers is $278$. The second number is $2$ less than $4$ times the first, and the third is $8$ more than $3$ times the first. Solution: The three numbers are $34, 134, 110$ ($8x+6=278 \implies x=34$)

Linear Inequality: $-9x+8+11x-12 > -4(-2x-8)$