Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{175x} +20 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 420x-175x& = & 20+84 \\\Leftrightarrow & \color{red}{245} x& = & 104 \\\Leftrightarrow & x = \frac{104}{245} & & \\ & V = \left\{ \frac{104}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{70x} +45 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 240x-70x& = & 45+24 \\\Leftrightarrow & \color{red}{170} x& = & 69 \\\Leftrightarrow & x = \frac{69}{170} & & \\ & V = \left\{ \frac{69}{170} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{66x} +6 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{+154} \\\Leftrightarrow & 693x-66x& = & 6+154 \\\Leftrightarrow & \color{red}{627} x& = & 160 \\\Leftrightarrow & x = \frac{160}{627} & & \\ & V = \left\{ \frac{160}{627} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+12} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -84x \color{red}{+12} \color{blue}{-12} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-12} \\\Leftrightarrow & -84x+98x& = & 21-12 \\\Leftrightarrow & \color{red}{14} x& = & 9 \\\Leftrightarrow & x = \frac{9}{14} & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{2})& = & 4x+\frac{3}{11} \\\Leftrightarrow & 15x-\frac{9}{2}& = & 4x+\frac{3}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{99}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{6}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-99} & = & \color{red}{88x} +6 \\\Leftrightarrow & 330x \color{red}{-99} \color{blue}{+99} \color{blue}{-88x} & = & \color{red}{88x} +6 \color{blue}{-88x} \color{blue}{+99} \\\Leftrightarrow & 330x-88x& = & 6+99 \\\Leftrightarrow & \color{red}{242} x& = & 105 \\\Leftrightarrow & x = \frac{105}{242} & & \\ & V = \left\{ \frac{105}{242} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+150} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 420x \color{red}{+150} \color{blue}{-150} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-150} \\\Leftrightarrow & 420x+245x& = & 42-150 \\\Leftrightarrow & \color{red}{665} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{665} & & \\ & V = \left\{ \frac{-108}{665} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{9})& = & 3x+\frac{5}{8} \\\Leftrightarrow & -35x+\frac{35}{9}& = & 3x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2520}{ \color{blue}{72} }x+ \frac{280}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2520x \color{red}{+280} & = & \color{red}{216x} +45 \\\Leftrightarrow & -2520x \color{red}{+280} \color{blue}{-280} \color{blue}{-216x} & = & \color{red}{216x} +45 \color{blue}{-216x} \color{blue}{-280} \\\Leftrightarrow & -2520x-216x& = & 45-280 \\\Leftrightarrow & \color{red}{-2736} x& = & -235 \\\Leftrightarrow & x = \frac{-235}{-2736} & & \\\Leftrightarrow & x = \frac{235}{2736} & & \\ & V = \left\{ \frac{235}{2736} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{96x} +16 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +16 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & -180x-96x& = & 16-45 \\\Leftrightarrow & \color{red}{-276} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-276} & & \\\Leftrightarrow & x = \frac{29}{276} & & \\ & V = \left\{ \frac{29}{276} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x-\frac{24}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-216} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -1890x \color{red}{-216} \color{blue}{+216} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+216} \\\Leftrightarrow & -1890x+441x& = & 14+216 \\\Leftrightarrow & \color{red}{-1449} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1449} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x+\frac{8}{11}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+8} & = & \color{red}{-77x} +5 \\\Leftrightarrow & -66x \color{red}{+8} \color{blue}{-8} \color{blue}{+77x} & = & \color{red}{-77x} +5 \color{blue}{+77x} \color{blue}{-8} \\\Leftrightarrow & -66x+77x& = & 5-8 \\\Leftrightarrow & \color{red}{11} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & -9x+\frac{5}{12} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-32} & = & \color{red}{-108x} +5 \\\Leftrightarrow & -240x \color{red}{-32} \color{blue}{+32} \color{blue}{+108x} & = & \color{red}{-108x} +5 \color{blue}{+108x} \color{blue}{+32} \\\Leftrightarrow & -240x+108x& = & 5+32 \\\Leftrightarrow & \color{red}{-132} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-132} & & \\\Leftrightarrow & x = \frac{-37}{132} & & \\ & V = \left\{ \frac{-37}{132} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{105x} +20 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+12} \\\Leftrightarrow & -90x-105x& = & 20+12 \\\Leftrightarrow & \color{red}{-195} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-195} & & \\\Leftrightarrow & x = \frac{-32}{195} & & \\ & V = \left\{ \frac{-32}{195} \right\} & \\\end{align}\)