Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(7(4x-\frac{4}{5})=-9x+\frac{4}{3}\)
2. \(6(-4x+\frac{4}{5})=5x+\frac{5}{11}\)
3. \(2(3x+\frac{4}{5})=-5x+\frac{5}{6}\)
4. \(6(5x+\frac{5}{11})=-7x+\frac{6}{5}\)
5. \(3(5x-\frac{4}{7})=-4x+\frac{10}{9}\)
6. \(-4(-2x+\frac{5}{9})=-5x+\frac{10}{7}\)
7. \(3(3x-\frac{3}{2})=-4x+\frac{2}{3}\)
8. \(4(-4x-\frac{4}{9})=-7x+\frac{7}{6}\)
9. \(-2(-3x+\frac{2}{9})=-7x+\frac{4}{7}\)
10. \(-5(-2x+\frac{2}{11})=-7x+\frac{5}{7}\)
11. \(-2(2x-\frac{2}{5})=5x+\frac{5}{11}\)
12. \(6(4x+\frac{4}{5})=5x+\frac{3}{2}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{5})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{28}{5}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-135x} +20 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{+84} \\\Leftrightarrow & 420x+135x& = & 20+84 \\\Leftrightarrow & \color{red}{555} x& = & 104 \\\Leftrightarrow & x = \frac{104}{555} & & \\ & V = \left\{ \frac{104}{555} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+264} & = & \color{red}{275x} +25 \\\Leftrightarrow & -1320x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & -1320x-275x& = & 25-264 \\\Leftrightarrow & \color{red}{-1595} x& = & -239 \\\Leftrightarrow & x = \frac{-239}{-1595} & & \\\Leftrightarrow & x = \frac{239}{1595} & & \\ & V = \left\{ \frac{239}{1595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 6x+\frac{8}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{+48} & = & \color{red}{-150x} +25 \\\Leftrightarrow & 180x \color{red}{+48} \color{blue}{-48} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-48} \\\Leftrightarrow & 180x+150x& = & 25-48 \\\Leftrightarrow & \color{red}{330} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{330} & & \\ & V = \left\{ \frac{-23}{330} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+150} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 1650x \color{red}{+150} \color{blue}{-150} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-150} \\\Leftrightarrow & 1650x+385x& = & 66-150 \\\Leftrightarrow & \color{red}{2035} x& = & -84 \\\Leftrightarrow & x = \frac{-84}{2035} & & \\ & V = \left\{ \frac{-84}{2035} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{7})& = & -4x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{12}{7}& = & -4x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{108}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-108} & = & \color{red}{-252x} +70 \\\Leftrightarrow & 945x \color{red}{-108} \color{blue}{+108} \color{blue}{+252x} & = & \color{red}{-252x} +70 \color{blue}{+252x} \color{blue}{+108} \\\Leftrightarrow & 945x+252x& = & 70+108 \\\Leftrightarrow & \color{red}{1197} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1197} & & \\ & V = \left\{ \frac{178}{1197} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{9})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{20}{9}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-140} & = & \color{red}{-315x} +90 \\\Leftrightarrow & 504x \color{red}{-140} \color{blue}{+140} \color{blue}{+315x} & = & \color{red}{-315x} +90 \color{blue}{+315x} \color{blue}{+140} \\\Leftrightarrow & 504x+315x& = & 90+140 \\\Leftrightarrow & \color{red}{819} x& = & 230 \\\Leftrightarrow & x = \frac{230}{819} & & \\ & V = \left\{ \frac{230}{819} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{2})& = & -4x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{9}{2}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{54}{ \color{blue}{6} }x- \frac{27}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 54x \color{red}{-27} & = & \color{red}{-24x} +4 \\\Leftrightarrow & 54x \color{red}{-27} \color{blue}{+27} \color{blue}{+24x} & = & \color{red}{-24x} +4 \color{blue}{+24x} \color{blue}{+27} \\\Leftrightarrow & 54x+24x& = & 4+27 \\\Leftrightarrow & \color{red}{78} x& = & 31 \\\Leftrightarrow & x = \frac{31}{78} & & \\ & V = \left\{ \frac{31}{78} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{9})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -16x-\frac{16}{9}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x- \frac{32}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{-32} & = & \color{red}{-126x} +21 \\\Leftrightarrow & -288x \color{red}{-32} \color{blue}{+32} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{+32} \\\Leftrightarrow & -288x+126x& = & 21+32 \\\Leftrightarrow & \color{red}{-162} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-162} & & \\\Leftrightarrow & x = \frac{-53}{162} & & \\ & V = \left\{ \frac{-53}{162} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-28} & = & \color{red}{-441x} +36 \\\Leftrightarrow & 378x \color{red}{-28} \color{blue}{+28} \color{blue}{+441x} & = & \color{red}{-441x} +36 \color{blue}{+441x} \color{blue}{+28} \\\Leftrightarrow & 378x+441x& = & 36+28 \\\Leftrightarrow & \color{red}{819} x& = & 64 \\\Leftrightarrow & x = \frac{64}{819} & & \\ & V = \left\{ \frac{64}{819} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-70} & = & \color{red}{-539x} +55 \\\Leftrightarrow & 770x \color{red}{-70} \color{blue}{+70} \color{blue}{+539x} & = & \color{red}{-539x} +55 \color{blue}{+539x} \color{blue}{+70} \\\Leftrightarrow & 770x+539x& = & 55+70 \\\Leftrightarrow & \color{red}{1309} x& = & 125 \\\Leftrightarrow & x = \frac{125}{1309} & & \\ & V = \left\{ \frac{125}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+44} & = & \color{red}{275x} +25 \\\Leftrightarrow & -220x \color{red}{+44} \color{blue}{-44} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-44} \\\Leftrightarrow & -220x-275x& = & 25-44 \\\Leftrightarrow & \color{red}{-495} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-495} & & \\\Leftrightarrow & x = \frac{19}{495} & & \\ & V = \left\{ \frac{19}{495} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{+48} & = & \color{red}{50x} +15 \\\Leftrightarrow & 240x \color{red}{+48} \color{blue}{-48} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-48} \\\Leftrightarrow & 240x-50x& = & 15-48 \\\Leftrightarrow & \color{red}{190} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{190} & & \\ & V = \left\{ \frac{-33}{190} \right\} & \\\end{align}\)