Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{4})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{-32x} +10 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{+32x} & = & \color{red}{-32x} +10 \color{blue}{+32x} \color{blue}{+15} \\\Leftrightarrow & -60x+32x& = & 10+15 \\\Leftrightarrow & \color{red}{-28} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-28} & & \\\Leftrightarrow & x = \frac{-25}{28} & & \\ & V = \left\{ \frac{-25}{28} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{12}{11}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{+24} & = & \color{red}{-198x} +77 \\\Leftrightarrow & -176x \color{red}{+24} \color{blue}{-24} \color{blue}{+198x} & = & \color{red}{-198x} +77 \color{blue}{+198x} \color{blue}{-24} \\\Leftrightarrow & -176x+198x& = & 77-24 \\\Leftrightarrow & \color{red}{22} x& = & 53 \\\Leftrightarrow & x = \frac{53}{22} & & \\ & V = \left\{ \frac{53}{22} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{147x} +14 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-48} \\\Leftrightarrow & -336x-147x& = & 14-48 \\\Leftrightarrow & \color{red}{-483} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-483} & & \\\Leftrightarrow & x = \frac{34}{483} & & \\ & V = \left\{ \frac{34}{483} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-50} & = & \color{red}{175x} +21 \\\Leftrightarrow & 210x \color{red}{-50} \color{blue}{+50} \color{blue}{-175x} & = & \color{red}{175x} +21 \color{blue}{-175x} \color{blue}{+50} \\\Leftrightarrow & 210x-175x& = & 21+50 \\\Leftrightarrow & \color{red}{35} x& = & 71 \\\Leftrightarrow & x = \frac{71}{35} & & \\ & V = \left\{ \frac{71}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{48x} +27 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{-48x} & = & \color{red}{48x} +27 \color{blue}{-48x} \color{blue}{+28} \\\Leftrightarrow & 210x-48x& = & 27+28 \\\Leftrightarrow & \color{red}{162} x& = & 55 \\\Leftrightarrow & x = \frac{55}{162} & & \\ & V = \left\{ \frac{55}{162} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{7})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 6x-\frac{8}{7}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{32}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-32} & = & \color{red}{196x} +49 \\\Leftrightarrow & 168x \color{red}{-32} \color{blue}{+32} \color{blue}{-196x} & = & \color{red}{196x} +49 \color{blue}{-196x} \color{blue}{+32} \\\Leftrightarrow & 168x-196x& = & 49+32 \\\Leftrightarrow & \color{red}{-28} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-28} & & \\\Leftrightarrow & x = \frac{-81}{28} & & \\ & V = \left\{ \frac{-81}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & 6x+\frac{3}{2} \\\Leftrightarrow & -18x-\frac{18}{5}& = & 6x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{60}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{60x} +15 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-60x} & = & \color{red}{60x} +15 \color{blue}{-60x} \color{blue}{+36} \\\Leftrightarrow & -180x-60x& = & 15+36 \\\Leftrightarrow & \color{red}{-240} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-240} & & \\\Leftrightarrow & x = \frac{-17}{80} & & \\ & V = \left\{ \frac{-17}{80} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{5})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{-8} & = & \color{red}{-90x} +15 \\\Leftrightarrow & 100x \color{red}{-8} \color{blue}{+8} \color{blue}{+90x} & = & \color{red}{-90x} +15 \color{blue}{+90x} \color{blue}{+8} \\\Leftrightarrow & 100x+90x& = & 15+8 \\\Leftrightarrow & \color{red}{190} x& = & 23 \\\Leftrightarrow & x = \frac{23}{190} & & \\ & V = \left\{ \frac{23}{190} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{8})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{15}{8}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-75} & = & \color{red}{200x} +12 \\\Leftrightarrow & -480x \color{red}{-75} \color{blue}{+75} \color{blue}{-200x} & = & \color{red}{200x} +12 \color{blue}{-200x} \color{blue}{+75} \\\Leftrightarrow & -480x-200x& = & 12+75 \\\Leftrightarrow & \color{red}{-680} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-680} & & \\\Leftrightarrow & x = \frac{-87}{680} & & \\ & V = \left\{ \frac{-87}{680} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{49x} +10 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -70x-49x& = & 10-6 \\\Leftrightarrow & \color{red}{-119} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-119} & & \\\Leftrightarrow & x = \frac{-4}{119} & & \\ & V = \left\{ \frac{-4}{119} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-20} & = & \color{red}{66x} +99 \\\Leftrightarrow & 440x \color{red}{-20} \color{blue}{+20} \color{blue}{-66x} & = & \color{red}{66x} +99 \color{blue}{-66x} \color{blue}{+20} \\\Leftrightarrow & 440x-66x& = & 99+20 \\\Leftrightarrow & \color{red}{374} x& = & 119 \\\Leftrightarrow & x = \frac{119}{374} & & \\\Leftrightarrow & x = \frac{7}{22} & & \\ & V = \left\{ \frac{7}{22} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{5})& = & 2x+\frac{7}{8} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 2x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{+96} & = & \color{red}{80x} +35 \\\Leftrightarrow & 360x \color{red}{+96} \color{blue}{-96} \color{blue}{-80x} & = & \color{red}{80x} +35 \color{blue}{-80x} \color{blue}{-96} \\\Leftrightarrow & 360x-80x& = & 35-96 \\\Leftrightarrow & \color{red}{280} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{280} & & \\ & V = \left\{ \frac{-61}{280} \right\} & \\\end{align}\)