Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & -9x+\frac{3}{11} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+88} & = & \color{red}{-891x} +27 \\\Leftrightarrow & -792x \color{red}{+88} \color{blue}{-88} \color{blue}{+891x} & = & \color{red}{-891x} +27 \color{blue}{+891x} \color{blue}{-88} \\\Leftrightarrow & -792x+891x& = & 27-88 \\\Leftrightarrow & \color{red}{99} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{99} & & \\ & V = \left\{ \frac{-61}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{7})& = & -8x+\frac{8}{11} \\\Leftrightarrow & -25x-\frac{20}{7}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{-220} & = & \color{red}{-616x} +56 \\\Leftrightarrow & -1925x \color{red}{-220} \color{blue}{+220} \color{blue}{+616x} & = & \color{red}{-616x} +56 \color{blue}{+616x} \color{blue}{+220} \\\Leftrightarrow & -1925x+616x& = & 56+220 \\\Leftrightarrow & \color{red}{-1309} x& = & 276 \\\Leftrightarrow & x = \frac{276}{-1309} & & \\\Leftrightarrow & x = \frac{-276}{1309} & & \\ & V = \left\{ \frac{-276}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-28} & = & \color{red}{-147x} +27 \\\Leftrightarrow & -210x \color{red}{-28} \color{blue}{+28} \color{blue}{+147x} & = & \color{red}{-147x} +27 \color{blue}{+147x} \color{blue}{+28} \\\Leftrightarrow & -210x+147x& = & 27+28 \\\Leftrightarrow & \color{red}{-63} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-63} & & \\\Leftrightarrow & x = \frac{-55}{63} & & \\ & V = \left\{ \frac{-55}{63} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 35x-\frac{21}{8}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{-231} & = & \color{red}{-792x} +32 \\\Leftrightarrow & 3080x \color{red}{-231} \color{blue}{+231} \color{blue}{+792x} & = & \color{red}{-792x} +32 \color{blue}{+792x} \color{blue}{+231} \\\Leftrightarrow & 3080x+792x& = & 32+231 \\\Leftrightarrow & \color{red}{3872} x& = & 263 \\\Leftrightarrow & x = \frac{263}{3872} & & \\ & V = \left\{ \frac{263}{3872} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{10})& = & 9x+\frac{7}{10} \\\Leftrightarrow & 35x+\frac{21}{10}& = & 9x+\frac{7}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+21} & = & \color{red}{90x} +7 \\\Leftrightarrow & 350x \color{red}{+21} \color{blue}{-21} \color{blue}{-90x} & = & \color{red}{90x} +7 \color{blue}{-90x} \color{blue}{-21} \\\Leftrightarrow & 350x-90x& = & 7-21 \\\Leftrightarrow & \color{red}{260} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{260} & & \\\Leftrightarrow & x = \frac{-7}{130} & & \\ & V = \left\{ \frac{-7}{130} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-54} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 594x \color{red}{-54} \color{blue}{+54} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+54} \\\Leftrightarrow & 594x+231x& = & 88+54 \\\Leftrightarrow & \color{red}{825} x& = & 142 \\\Leftrightarrow & x = \frac{142}{825} & & \\ & V = \left\{ \frac{142}{825} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{5}{7} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-196} & = & \color{red}{-168x} +15 \\\Leftrightarrow & -441x \color{red}{-196} \color{blue}{+196} \color{blue}{+168x} & = & \color{red}{-168x} +15 \color{blue}{+168x} \color{blue}{+196} \\\Leftrightarrow & -441x+168x& = & 15+196 \\\Leftrightarrow & \color{red}{-273} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-273} & & \\\Leftrightarrow & x = \frac{-211}{273} & & \\ & V = \left\{ \frac{-211}{273} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1008}{ \color{blue}{84} }x+ \frac{360}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1008x \color{red}{+360} & = & \color{red}{-420x} +35 \\\Leftrightarrow & -1008x \color{red}{+360} \color{blue}{-360} \color{blue}{+420x} & = & \color{red}{-420x} +35 \color{blue}{+420x} \color{blue}{-360} \\\Leftrightarrow & -1008x+420x& = & 35-360 \\\Leftrightarrow & \color{red}{-588} x& = & -325 \\\Leftrightarrow & x = \frac{-325}{-588} & & \\\Leftrightarrow & x = \frac{325}{588} & & \\ & V = \left\{ \frac{325}{588} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 8x-\frac{16}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{320}{ \color{blue}{40} }x- \frac{128}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 320x \color{red}{-128} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 320x \color{red}{-128} \color{blue}{+128} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+128} \\\Leftrightarrow & 320x+280x& = & 35+128 \\\Leftrightarrow & \color{red}{600} x& = & 163 \\\Leftrightarrow & x = \frac{163}{600} & & \\ & V = \left\{ \frac{163}{600} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & 8x+\frac{8}{9} \\\Leftrightarrow & 25x-\frac{10}{7}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{-90} & = & \color{red}{504x} +56 \\\Leftrightarrow & 1575x \color{red}{-90} \color{blue}{+90} \color{blue}{-504x} & = & \color{red}{504x} +56 \color{blue}{-504x} \color{blue}{+90} \\\Leftrightarrow & 1575x-504x& = & 56+90 \\\Leftrightarrow & \color{red}{1071} x& = & 146 \\\Leftrightarrow & x = \frac{146}{1071} & & \\ & V = \left\{ \frac{146}{1071} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{420}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{350x} +49 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-350x} & = & \color{red}{350x} +49 \color{blue}{-350x} \color{blue}{+60} \\\Leftrightarrow & 420x-350x& = & 49+60 \\\Leftrightarrow & \color{red}{70} x& = & 109 \\\Leftrightarrow & x = \frac{109}{70} & & \\ & V = \left\{ \frac{109}{70} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-140} & = & \color{red}{-147x} +12 \\\Leftrightarrow & -420x \color{red}{-140} \color{blue}{+140} \color{blue}{+147x} & = & \color{red}{-147x} +12 \color{blue}{+147x} \color{blue}{+140} \\\Leftrightarrow & -420x+147x& = & 12+140 \\\Leftrightarrow & \color{red}{-273} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-273} & & \\\Leftrightarrow & x = \frac{-152}{273} & & \\ & V = \left\{ \frac{-152}{273} \right\} & \\\end{align}\)