Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{9})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-140} & = & \color{red}{189x} +54 \\\Leftrightarrow & 1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-189x} & = & \color{red}{189x} +54 \color{blue}{-189x} \color{blue}{+140} \\\Leftrightarrow & 1260x-189x& = & 54+140 \\\Leftrightarrow & \color{red}{1071} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1071} & & \\ & V = \left\{ \frac{194}{1071} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+90} & = & \color{red}{441x} +28 \\\Leftrightarrow & 1260x \color{red}{+90} \color{blue}{-90} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{-90} \\\Leftrightarrow & 1260x-441x& = & 28-90 \\\Leftrightarrow & \color{red}{819} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{819} & & \\ & V = \left\{ \frac{-62}{819} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{+90} & = & \color{red}{567x} +70 \\\Leftrightarrow & -1575x \color{red}{+90} \color{blue}{-90} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{-90} \\\Leftrightarrow & -1575x-567x& = & 70-90 \\\Leftrightarrow & \color{red}{-2142} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-2142} & & \\\Leftrightarrow & x = \frac{10}{1071} & & \\ & V = \left\{ \frac{10}{1071} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+110} & = & \color{red}{231x} +28 \\\Leftrightarrow & 616x \color{red}{+110} \color{blue}{-110} \color{blue}{-231x} & = & \color{red}{231x} +28 \color{blue}{-231x} \color{blue}{-110} \\\Leftrightarrow & 616x-231x& = & 28-110 \\\Leftrightarrow & \color{red}{385} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{385} & & \\ & V = \left\{ \frac{-82}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-8} & = & \color{red}{-9x} +8 \\\Leftrightarrow & -60x \color{red}{-8} \color{blue}{+8} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{+8} \\\Leftrightarrow & -60x+9x& = & 8+8 \\\Leftrightarrow & \color{red}{-51} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-51} & & \\\Leftrightarrow & x = \frac{-16}{51} & & \\ & V = \left\{ \frac{-16}{51} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{3})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-88} & = & \color{red}{-231x} +15 \\\Leftrightarrow & -198x \color{red}{-88} \color{blue}{+88} \color{blue}{+231x} & = & \color{red}{-231x} +15 \color{blue}{+231x} \color{blue}{+88} \\\Leftrightarrow & -198x+231x& = & 15+88 \\\Leftrightarrow & \color{red}{33} x& = & 103 \\\Leftrightarrow & x = \frac{103}{33} & & \\ & V = \left\{ \frac{103}{33} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{11})& = & 4x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{20}{11}& = & 4x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+20} & = & \color{red}{44x} +2 \\\Leftrightarrow & -165x \color{red}{+20} \color{blue}{-20} \color{blue}{-44x} & = & \color{red}{44x} +2 \color{blue}{-44x} \color{blue}{-20} \\\Leftrightarrow & -165x-44x& = & 2-20 \\\Leftrightarrow & \color{red}{-209} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-209} & & \\\Leftrightarrow & x = \frac{18}{209} & & \\ & V = \left\{ \frac{18}{209} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{9})& = & 2x+\frac{5}{7} \\\Leftrightarrow & 21x-\frac{14}{9}& = & 2x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1323}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1323x \color{red}{-98} & = & \color{red}{126x} +45 \\\Leftrightarrow & 1323x \color{red}{-98} \color{blue}{+98} \color{blue}{-126x} & = & \color{red}{126x} +45 \color{blue}{-126x} \color{blue}{+98} \\\Leftrightarrow & 1323x-126x& = & 45+98 \\\Leftrightarrow & \color{red}{1197} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1197} & & \\ & V = \left\{ \frac{143}{1197} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -660x+275x& = & 10-132 \\\Leftrightarrow & \color{red}{-385} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-385} & & \\\Leftrightarrow & x = \frac{122}{385} & & \\ & V = \left\{ \frac{122}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 30x-\frac{12}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{-36} & = & \color{red}{-147x} +28 \\\Leftrightarrow & 630x \color{red}{-36} \color{blue}{+36} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+36} \\\Leftrightarrow & 630x+147x& = & 28+36 \\\Leftrightarrow & \color{red}{777} x& = & 64 \\\Leftrightarrow & x = \frac{64}{777} & & \\ & V = \left\{ \frac{64}{777} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{11})& = & -4x+\frac{6}{7} \\\Leftrightarrow & -15x-\frac{9}{11}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{63}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-63} & = & \color{red}{-308x} +66 \\\Leftrightarrow & -1155x \color{red}{-63} \color{blue}{+63} \color{blue}{+308x} & = & \color{red}{-308x} +66 \color{blue}{+308x} \color{blue}{+63} \\\Leftrightarrow & -1155x+308x& = & 66+63 \\\Leftrightarrow & \color{red}{-847} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-847} & & \\\Leftrightarrow & x = \frac{-129}{847} & & \\ & V = \left\{ \frac{-129}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & -6x+\frac{9}{10} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -6x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x- \frac{350}{ \color{blue}{30} })& = & (\frac{-180}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{-350} & = & \color{red}{-180x} +27 \\\Leftrightarrow & -1050x \color{red}{-350} \color{blue}{+350} \color{blue}{+180x} & = & \color{red}{-180x} +27 \color{blue}{+180x} \color{blue}{+350} \\\Leftrightarrow & -1050x+180x& = & 27+350 \\\Leftrightarrow & \color{red}{-870} x& = & 377 \\\Leftrightarrow & x = \frac{377}{-870} & & \\\Leftrightarrow & x = \frac{-13}{30} & & \\ & V = \left\{ \frac{-13}{30} \right\} & \\\end{align}\)