Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{11})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{16}{11}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-32} & = & \color{red}{198x} +99 \\\Leftrightarrow & 440x \color{red}{-32} \color{blue}{+32} \color{blue}{-198x} & = & \color{red}{198x} +99 \color{blue}{-198x} \color{blue}{+32} \\\Leftrightarrow & 440x-198x& = & 99+32 \\\Leftrightarrow & \color{red}{242} x& = & 131 \\\Leftrightarrow & x = \frac{131}{242} & & \\ & V = \left\{ \frac{131}{242} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{11})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{16}{11}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-112} & = & \color{red}{-693x} +88 \\\Leftrightarrow & 1540x \color{red}{-112} \color{blue}{+112} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{+112} \\\Leftrightarrow & 1540x+693x& = & 88+112 \\\Leftrightarrow & \color{red}{2233} x& = & 200 \\\Leftrightarrow & x = \frac{200}{2233} & & \\ & V = \left\{ \frac{200}{2233} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +20 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 20+36 \\\Leftrightarrow & \color{red}{-255} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-255} & & \\\Leftrightarrow & x = \frac{-56}{255} & & \\ & V = \left\{ \frac{-56}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{12}{11}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-24} & = & \color{red}{66x} +55 \\\Leftrightarrow & 440x \color{red}{-24} \color{blue}{+24} \color{blue}{-66x} & = & \color{red}{66x} +55 \color{blue}{-66x} \color{blue}{+24} \\\Leftrightarrow & 440x-66x& = & 55+24 \\\Leftrightarrow & \color{red}{374} x& = & 79 \\\Leftrightarrow & x = \frac{79}{374} & & \\ & V = \left\{ \frac{79}{374} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & -8x+\frac{3}{7} \\\Leftrightarrow & 21x+\frac{14}{5}& = & -8x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{+98} & = & \color{red}{-280x} +15 \\\Leftrightarrow & 735x \color{red}{+98} \color{blue}{-98} \color{blue}{+280x} & = & \color{red}{-280x} +15 \color{blue}{+280x} \color{blue}{-98} \\\Leftrightarrow & 735x+280x& = & 15-98 \\\Leftrightarrow & \color{red}{1015} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{1015} & & \\ & V = \left\{ \frac{-83}{1015} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{360}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 360x \color{red}{+72} & = & \color{red}{-150x} +25 \\\Leftrightarrow & 360x \color{red}{+72} \color{blue}{-72} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-72} \\\Leftrightarrow & 360x+150x& = & 25-72 \\\Leftrightarrow & \color{red}{510} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{510} & & \\ & V = \left\{ \frac{-47}{510} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{8})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -10x-\frac{15}{8}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{616x} +32 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{-616x} & = & \color{red}{616x} +32 \color{blue}{-616x} \color{blue}{+165} \\\Leftrightarrow & -880x-616x& = & 32+165 \\\Leftrightarrow & \color{red}{-1496} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1496} & & \\\Leftrightarrow & x = \frac{-197}{1496} & & \\ & V = \left\{ \frac{-197}{1496} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-49x} +3 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -168x+49x& = & 3-30 \\\Leftrightarrow & \color{red}{-119} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-119} & & \\\Leftrightarrow & x = \frac{27}{119} & & \\ & V = \left\{ \frac{27}{119} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{189x} +56 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-30} \\\Leftrightarrow & 210x-189x& = & 56-30 \\\Leftrightarrow & \color{red}{21} x& = & 26 \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{10})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 28x-\frac{21}{10}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x- \frac{21}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{-21} & = & \color{red}{-30x} +12 \\\Leftrightarrow & 280x \color{red}{-21} \color{blue}{+21} \color{blue}{+30x} & = & \color{red}{-30x} +12 \color{blue}{+30x} \color{blue}{+21} \\\Leftrightarrow & 280x+30x& = & 12+21 \\\Leftrightarrow & \color{red}{310} x& = & 33 \\\Leftrightarrow & x = \frac{33}{310} & & \\ & V = \left\{ \frac{33}{310} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{-140x} +16 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +16 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -120x+140x& = & 16+75 \\\Leftrightarrow & \color{red}{20} x& = & 91 \\\Leftrightarrow & x = \frac{91}{20} & & \\ & V = \left\{ \frac{91}{20} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+42} & = & \color{red}{-81x} +10 \\\Leftrightarrow & -315x \color{red}{+42} \color{blue}{-42} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{-42} \\\Leftrightarrow & -315x+81x& = & 10-42 \\\Leftrightarrow & \color{red}{-234} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-234} & & \\\Leftrightarrow & x = \frac{16}{117} & & \\ & V = \left\{ \frac{16}{117} \right\} & \\\end{align}\)