Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{2})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 6x-\frac{15}{2}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 2 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{90}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-90} & = & \color{red}{-84x} +7 \\\Leftrightarrow & 72x \color{red}{-90} \color{blue}{+90} \color{blue}{+84x} & = & \color{red}{-84x} +7 \color{blue}{+84x} \color{blue}{+90} \\\Leftrightarrow & 72x+84x& = & 7+90 \\\Leftrightarrow & \color{red}{156} x& = & 97 \\\Leftrightarrow & x = \frac{97}{156} & & \\ & V = \left\{ \frac{97}{156} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-154} & = & \color{red}{264x} +30 \\\Leftrightarrow & -693x \color{red}{-154} \color{blue}{+154} \color{blue}{-264x} & = & \color{red}{264x} +30 \color{blue}{-264x} \color{blue}{+154} \\\Leftrightarrow & -693x-264x& = & 30+154 \\\Leftrightarrow & \color{red}{-957} x& = & 184 \\\Leftrightarrow & x = \frac{184}{-957} & & \\\Leftrightarrow & x = \frac{-184}{957} & & \\ & V = \left\{ \frac{-184}{957} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{9})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{8}{9}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+88} & = & \color{red}{-495x} +27 \\\Leftrightarrow & 1188x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +27 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & 1188x+495x& = & 27-88 \\\Leftrightarrow & \color{red}{1683} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{1683} & & \\ & V = \left\{ \frac{-61}{1683} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{2})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 9x+\frac{9}{2}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+45} & = & \color{red}{-50x} +16 \\\Leftrightarrow & 90x \color{red}{+45} \color{blue}{-45} \color{blue}{+50x} & = & \color{red}{-50x} +16 \color{blue}{+50x} \color{blue}{-45} \\\Leftrightarrow & 90x+50x& = & 16-45 \\\Leftrightarrow & \color{red}{140} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{140} & & \\ & V = \left\{ \frac{-29}{140} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{3})& = & 4x+\frac{9}{11} \\\Leftrightarrow & 15x-\frac{10}{3}& = & 4x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-110} & = & \color{red}{132x} +27 \\\Leftrightarrow & 495x \color{red}{-110} \color{blue}{+110} \color{blue}{-132x} & = & \color{red}{132x} +27 \color{blue}{-132x} \color{blue}{+110} \\\Leftrightarrow & 495x-132x& = & 27+110 \\\Leftrightarrow & \color{red}{363} x& = & 137 \\\Leftrightarrow & x = \frac{137}{363} & & \\ & V = \left\{ \frac{137}{363} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -4x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{+108} & = & \color{red}{-180x} +20 \\\Leftrightarrow & -675x \color{red}{+108} \color{blue}{-108} \color{blue}{+180x} & = & \color{red}{-180x} +20 \color{blue}{+180x} \color{blue}{-108} \\\Leftrightarrow & -675x+180x& = & 20-108 \\\Leftrightarrow & \color{red}{-495} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-495} & & \\\Leftrightarrow & x = \frac{8}{45} & & \\ & V = \left\{ \frac{8}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & -420x+147x& = & 56+60 \\\Leftrightarrow & \color{red}{-273} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-273} & & \\\Leftrightarrow & x = \frac{-116}{273} & & \\ & V = \left\{ \frac{-116}{273} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-10} & = & \color{red}{77x} +5 \\\Leftrightarrow & 220x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & 220x-77x& = & 5+10 \\\Leftrightarrow & \color{red}{143} x& = & 15 \\\Leftrightarrow & x = \frac{15}{143} & & \\ & V = \left\{ \frac{15}{143} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{-140x} +16 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +16 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -400x+140x& = & 16+75 \\\Leftrightarrow & \color{red}{-260} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-260} & & \\\Leftrightarrow & x = \frac{-7}{20} & & \\ & V = \left\{ \frac{-7}{20} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & 4x+\frac{8}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{80x} +32 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{-80x} & = & \color{red}{80x} +32 \color{blue}{-80x} \color{blue}{-75} \\\Leftrightarrow & -300x-80x& = & 32-75 \\\Leftrightarrow & \color{red}{-380} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-380} & & \\\Leftrightarrow & x = \frac{43}{380} & & \\ & V = \left\{ \frac{43}{380} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1890x \color{red}{-270} & = & \color{red}{441x} +28 \\\Leftrightarrow & 1890x \color{red}{-270} \color{blue}{+270} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{+270} \\\Leftrightarrow & 1890x-441x& = & 28+270 \\\Leftrightarrow & \color{red}{1449} x& = & 298 \\\Leftrightarrow & x = \frac{298}{1449} & & \\ & V = \left\{ \frac{298}{1449} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -4x+\frac{2}{5} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -4x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{-75} & = & \color{red}{-80x} +8 \\\Leftrightarrow & 500x \color{red}{-75} \color{blue}{+75} \color{blue}{+80x} & = & \color{red}{-80x} +8 \color{blue}{+80x} \color{blue}{+75} \\\Leftrightarrow & 500x+80x& = & 8+75 \\\Leftrightarrow & \color{red}{580} x& = & 83 \\\Leftrightarrow & x = \frac{83}{580} & & \\ & V = \left\{ \frac{83}{580} \right\} & \\\end{align}\)