Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{5})& = & 8x+\frac{4}{7} \\\Leftrightarrow & -21x+\frac{14}{5}& = & 8x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-735}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -735x \color{red}{+98} & = & \color{red}{280x} +20 \\\Leftrightarrow & -735x \color{red}{+98} \color{blue}{-98} \color{blue}{-280x} & = & \color{red}{280x} +20 \color{blue}{-280x} \color{blue}{-98} \\\Leftrightarrow & -735x-280x& = & 20-98 \\\Leftrightarrow & \color{red}{-1015} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{-1015} & & \\\Leftrightarrow & x = \frac{78}{1015} & & \\ & V = \left\{ \frac{78}{1015} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 24x-\frac{24}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{960}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 960x \color{red}{-192} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 960x \color{red}{-192} \color{blue}{+192} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{+192} \\\Leftrightarrow & 960x+200x& = & 35+192 \\\Leftrightarrow & \color{red}{1160} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1160} & & \\ & V = \left\{ \frac{227}{1160} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+60} \\\Leftrightarrow & 420x-175x& = & 42+60 \\\Leftrightarrow & \color{red}{245} x& = & 102 \\\Leftrightarrow & x = \frac{102}{245} & & \\ & V = \left\{ \frac{102}{245} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -24x-\frac{24}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x- \frac{240}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{-240} & = & \color{red}{550x} +99 \\\Leftrightarrow & -2640x \color{red}{-240} \color{blue}{+240} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{+240} \\\Leftrightarrow & -2640x-550x& = & 99+240 \\\Leftrightarrow & \color{red}{-3190} x& = & 339 \\\Leftrightarrow & x = \frac{339}{-3190} & & \\\Leftrightarrow & x = \frac{-339}{3190} & & \\ & V = \left\{ \frac{-339}{3190} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-16} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -140x \color{red}{-16} \color{blue}{+16} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+16} \\\Leftrightarrow & -140x+49x& = & 10+16 \\\Leftrightarrow & \color{red}{-91} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-91} & & \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1890x \color{red}{-270} & = & \color{red}{441x} +28 \\\Leftrightarrow & 1890x \color{red}{-270} \color{blue}{+270} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{+270} \\\Leftrightarrow & 1890x-441x& = & 28+270 \\\Leftrightarrow & \color{red}{1449} x& = & 298 \\\Leftrightarrow & x = \frac{298}{1449} & & \\ & V = \left\{ \frac{298}{1449} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -16x-\frac{12}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{-60} & = & \color{red}{245x} +49 \\\Leftrightarrow & -560x \color{red}{-60} \color{blue}{+60} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{+60} \\\Leftrightarrow & -560x-245x& = & 49+60 \\\Leftrightarrow & \color{red}{-805} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-805} & & \\\Leftrightarrow & x = \frac{-109}{805} & & \\ & V = \left\{ \frac{-109}{805} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & 8x+\frac{5}{6} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 8x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{192x} +20 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{-192x} & = & \color{red}{192x} +20 \color{blue}{-192x} \color{blue}{-63} \\\Leftrightarrow & 504x-192x& = & 20-63 \\\Leftrightarrow & \color{red}{312} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{312} & & \\ & V = \left\{ \frac{-43}{312} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 3x+\frac{3}{8} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{128}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-128} & = & \color{red}{168x} +21 \\\Leftrightarrow & -1120x \color{red}{-128} \color{blue}{+128} \color{blue}{-168x} & = & \color{red}{168x} +21 \color{blue}{-168x} \color{blue}{+128} \\\Leftrightarrow & -1120x-168x& = & 21+128 \\\Leftrightarrow & \color{red}{-1288} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1288} & & \\\Leftrightarrow & x = \frac{-149}{1288} & & \\ & V = \left\{ \frac{-149}{1288} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{21x} +4 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & 60x-21x& = & 4-20 \\\Leftrightarrow & \color{red}{39} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{39} & & \\ & V = \left\{ \frac{-16}{39} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{9})& = & -9x+\frac{4}{9} \\\Leftrightarrow & -35x+\frac{28}{9}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+28} & = & \color{red}{-81x} +4 \\\Leftrightarrow & -315x \color{red}{+28} \color{blue}{-28} \color{blue}{+81x} & = & \color{red}{-81x} +4 \color{blue}{+81x} \color{blue}{-28} \\\Leftrightarrow & -315x+81x& = & 4-28 \\\Leftrightarrow & \color{red}{-234} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-234} & & \\\Leftrightarrow & x = \frac{4}{39} & & \\ & V = \left\{ \frac{4}{39} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{-32} & = & \color{red}{-198x} +99 \\\Leftrightarrow & -176x \color{red}{-32} \color{blue}{+32} \color{blue}{+198x} & = & \color{red}{-198x} +99 \color{blue}{+198x} \color{blue}{+32} \\\Leftrightarrow & -176x+198x& = & 99+32 \\\Leftrightarrow & \color{red}{22} x& = & 131 \\\Leftrightarrow & x = \frac{131}{22} & & \\ & V = \left\{ \frac{131}{22} \right\} & \\\end{align}\)