Test 3

CORRECTIONS EX BY TOTAL 220 98 MAT 092 Beginning Algebra NAME: KEY Test #3 1. State whether the following statements are TRUE or FALSE. No explanation is needed for this part. FALSE (A) \(\frac{70u}{-5x+2=-(5x-2)}\) FALSE \[-5x+2\] 1 B) \[\frac{3+12x}{4}=3+3x\] C) \(5x+4x=9x^{2}\) \[9\times f9x^{4}\] \[\frac{3}{4}+\frac{12}{4}x=\frac{3}{4}+3x\] D) 45% fraction \[\frac{45}{100+5}=\frac{9}{20}\] \[\frac{9}{20}\] TRU (E) The represents 3.75% THE \[\frac{3.75}{100}=.0371\] 1F) The inequality \(-2\ge x\) corresponds notation \((-\infty,-2]\) TRUE (1G) The ordered pair (2,1) is a solution to the equation \(x-2y=0\) 2 2-2(1) TRUE 2-2 2. Solve the following equations. To receive full credit, you must show your work. 4) \(2(x+2)-(4x-3)=5x+1\) 4 \[2x+4-4x+3=5x+1\] 13) \(\frac{4x+16}{8}\times\frac{x+4}{2}\) \[-2x+7=5x+1\] \[2(4x+10)=8(x+4)\] -5x -7 \[8x+32=8x+32\] \[-5x-7\] IDENTITY \(x=\underline{ACCmad~H^{\prime}s}\) \[\frac{-7x}{-7}=\frac{-6}{7}\] \[x=\frac{6}{7}\] C) \(4(x-1)-3(x+2)=x-8\) \[4x-4-3x-6=x-8\] \[x-10=x-8\] -x+10 \[D=2\] CONTRADICTION \[10\underline{50k\sqrt{riol}}_{12}\] 2+ XI 4 \[\frac{1}{6}x-\frac{3}{4}=\frac{2}{3}x+\frac{1}{2}\] \[\frac{12}{1}(\frac{1}{6}x-\frac{3}{4})=\frac{12}{1}(\frac{2}{3}x+\frac{1}{2})\] \[2x-9=8x+6\] \[\frac{-6x}{-6}=\frac{15}{26}\] \[x=\frac{-5}{2}\] E) \(5x+4+2(x-3)=3(x+4)-12\) \[0.5x+0.4=0.75\] \[5x+4+2x-6=3x+12-12\] \[100\underline{(0.5x+0.7)=100(0.7y)\] \[7x-2=3x\] \[0x+40=\] \[\frac{-2}{-4}=\frac{-4x}{-4}\] \[-q0-q0\] \[\underline{x=\frac{1}{2}}_{a}\] 3. Solve the following formulas for the indicated variable. Please show your work. A) \(C=2\pi r\) solve for r. \[\frac{c}{2\pi}=\frac{2\pi r}{2\pi}\] \[r=\frac{c}{2\pi}\] B) \(3x+4y=12\) solve for y. \[-3x+4y=12\] \[\frac{4y}{4}=\frac{-3x+12}{4}\] \[y=-\frac{3}{4}x+3\] C) \(A=\frac{x+y+z}{3}\) solve for y. \[3A=3(\frac{x+y+z}{3})\] \[3A=x+y+x\] -x-z \[y=3A-x-z\] 4. Solve the following three inequalities. Put your answers in INTERVAL NOTATION. A) \(4x+5<2x-9\) -2x-5 \[\frac{2x}{2}<-\frac{14}{2}\] \[x<-7\] \[(-\infty,-7)\] B) \(3x+2(x-1)\ge3(2-x)-4\) \[3x+2x-2\ge6-3x-4\] \[5x-2\ge-3x+2\] +3x+2 \[\frac{8x}{8}\ge\frac{4}{8}\] \[x\ge\frac{1}{2}\] \[[\frac{1}{2},\infty)\] C) \(3-\frac{3}{4}x>6\) \[-\frac{3}{4}x>3\] \[-\frac{4}{3}(-\frac{3}{4}x)<-\frac{4}{3}(3)\] \[x<-8\] \[(-\infty,-8)\] 5. For the set of numbers given by the inequality \((-\infty,\frac{3}{2})\), do the following: A) Graph the set on a number line. [Image of a number line with an open circle at 3/2 and shading to the left] B) Rewrite the set as an inequality. \[x\le\frac{3}{2}\] OR \[\frac{3}{2}\ge x\]