Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-84} & = & \color{red}{-280x} +20 \\\Leftrightarrow & -525x \color{red}{-84} \color{blue}{+84} \color{blue}{+280x} & = & \color{red}{-280x} +20 \color{blue}{+280x} \color{blue}{+84} \\\Leftrightarrow & -525x+280x& = & 20+84 \\\Leftrightarrow & \color{red}{-245} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-245} & & \\\Leftrightarrow & x = \frac{-104}{245} & & \\ & V = \left\{ \frac{-104}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & 2x+\frac{3}{8} \\\Leftrightarrow & -25x-\frac{10}{7}& = & 2x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1400}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{112}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1400x \color{red}{-80} & = & \color{red}{112x} +21 \\\Leftrightarrow & -1400x \color{red}{-80} \color{blue}{+80} \color{blue}{-112x} & = & \color{red}{112x} +21 \color{blue}{-112x} \color{blue}{+80} \\\Leftrightarrow & -1400x-112x& = & 21+80 \\\Leftrightarrow & \color{red}{-1512} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-1512} & & \\\Leftrightarrow & x = \frac{-101}{1512} & & \\ & V = \left\{ \frac{-101}{1512} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{4})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -28x+\frac{21}{4}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-560}{ \color{blue}{20} }x+ \frac{105}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{160x} +18 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{-160x} & = & \color{red}{160x} +18 \color{blue}{-160x} \color{blue}{-105} \\\Leftrightarrow & -560x-160x& = & 18-105 \\\Leftrightarrow & \color{red}{-720} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-720} & & \\\Leftrightarrow & x = \frac{29}{240} & & \\ & V = \left\{ \frac{29}{240} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 30x+\frac{12}{11}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{+108} & = & \color{red}{693x} +55 \\\Leftrightarrow & 2970x \color{red}{+108} \color{blue}{-108} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{-108} \\\Leftrightarrow & 2970x-693x& = & 55-108 \\\Leftrightarrow & \color{red}{2277} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{2277} & & \\ & V = \left\{ \frac{-53}{2277} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 6x+\frac{4}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+8} & = & \color{red}{-50x} +25 \\\Leftrightarrow & 60x \color{red}{+8} \color{blue}{-8} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{-8} \\\Leftrightarrow & 60x+50x& = & 25-8 \\\Leftrightarrow & \color{red}{110} x& = & 17 \\\Leftrightarrow & x = \frac{17}{110} & & \\ & V = \left\{ \frac{17}{110} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{11})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -28x-\frac{35}{11}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2156}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2156x \color{red}{-245} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -2156x \color{red}{-245} \color{blue}{+245} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+245} \\\Leftrightarrow & -2156x+231x& = & 88+245 \\\Leftrightarrow & \color{red}{-1925} x& = & 333 \\\Leftrightarrow & x = \frac{333}{-1925} & & \\\Leftrightarrow & x = \frac{-333}{1925} & & \\ & V = \left\{ \frac{-333}{1925} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+88} & = & \color{red}{-297x} +15 \\\Leftrightarrow & 264x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & 264x+297x& = & 15-88 \\\Leftrightarrow & \color{red}{561} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{561} & & \\ & V = \left\{ \frac{-73}{561} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{25}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{990}{ \color{blue}{66} }x+ \frac{150}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 990x \color{red}{+150} & = & \color{red}{-462x} +55 \\\Leftrightarrow & 990x \color{red}{+150} \color{blue}{-150} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{-150} \\\Leftrightarrow & 990x+462x& = & 55-150 \\\Leftrightarrow & \color{red}{1452} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{1452} & & \\ & V = \left\{ \frac{-95}{1452} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{3})& = & 2x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-140} & = & \color{red}{42x} +24 \\\Leftrightarrow & 315x \color{red}{-140} \color{blue}{+140} \color{blue}{-42x} & = & \color{red}{42x} +24 \color{blue}{-42x} \color{blue}{+140} \\\Leftrightarrow & 315x-42x& = & 24+140 \\\Leftrightarrow & \color{red}{273} x& = & 164 \\\Leftrightarrow & x = \frac{164}{273} & & \\ & V = \left\{ \frac{164}{273} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -180x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{-255} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-255} & & \\\Leftrightarrow & x = \frac{-4}{255} & & \\ & V = \left\{ \frac{-4}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{-88} & = & \color{red}{-495x} +54 \\\Leftrightarrow & -396x \color{red}{-88} \color{blue}{+88} \color{blue}{+495x} & = & \color{red}{-495x} +54 \color{blue}{+495x} \color{blue}{+88} \\\Leftrightarrow & -396x+495x& = & 54+88 \\\Leftrightarrow & \color{red}{99} x& = & 142 \\\Leftrightarrow & x = \frac{142}{99} & & \\ & V = \left\{ \frac{142}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 9x+\frac{3}{8} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{160}{ \color{blue}{40} }x- \frac{32}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 160x \color{red}{-32} & = & \color{red}{360x} +15 \\\Leftrightarrow & 160x \color{red}{-32} \color{blue}{+32} \color{blue}{-360x} & = & \color{red}{360x} +15 \color{blue}{-360x} \color{blue}{+32} \\\Leftrightarrow & 160x-360x& = & 15+32 \\\Leftrightarrow & \color{red}{-200} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-200} & & \\\Leftrightarrow & x = \frac{-47}{200} & & \\ & V = \left\{ \frac{-47}{200} \right\} & \\\end{align}\)